KR101204677B1 - Method for correcting cirtical dimension uniformity - Google Patents

Abstract

The line width uniformity correction method of the present invention includes selecting a representative pattern density for line width uniformity correction, creating a correction map for at least one error component among the line width uniformity error components of the selected representative pattern density, and the representative pattern. Calculating a relationship between the density correction map and another pattern density.

Description

Method for correcting cirtical dimension uniformity

The present invention relates to a method for correcting a line width uniformity of a mask, and more particularly, to a method for correcting a line width uniformity that can control a line width uniformity regardless of a pattern density.

A number of lithographic processes are performed to form devices of fine size on a semiconductor substrate. For such a lithography process, a photomask having a fine pattern is essential. The photomask serves to form a desired pattern on the wafer while irradiating light to a mask pattern formed on the transparent substrate, and selectively transmitting light is transferred to the wafer. Such photomasks are generally manufactured using an electron beam lithography method.

The critical dimension (CD) of the mask pattern of the photomask is affected by exposure, development, and etching processes in the process of manufacturing the photomask. The CD Uniformity (CDU) of the photomask has to be managed with great precision because it directly affects the Linewidth Uniformity of the pattern on the wafer being transferred.

However, the conventional photomask line width uniformity correction method does not provide a correction method that can be applied to various pattern densities. As a result, all photomasks are costly and time-consuming because they have to feed back the results of the process once.

An object of the present invention is to provide a line width uniformity correction method that can be applied regardless of the pattern density.

Another object of the present invention is to provide a line width uniformity correction method capable of correcting line width uniformity of an asymmetrical component regardless of pattern density.

Still another object of the present invention is to provide a method for correcting line width uniformity, which can reduce the cost and time by simply correcting the line width uniformity of a photomask.

The line width uniformity correction method according to an embodiment of the present invention includes selecting a representative pattern density for line width uniformity correction, and generating a correction map for at least one error component among the line width uniformity error components of the selected representative pattern density. And calculating a relationship between the representative pattern density correction map and another pattern density correction map.

In an embodiment, the step of selecting a representative pattern density for the line width uniformity correction may include measuring line widths for a plurality of pattern densities, extracting line width error components based on the measured line widths, and extracting the line widths. The method may include analyzing correlations between pattern densities of error components.

In an embodiment, in the step of generating a correction map for any one or more error components of the selected representative pattern density, the error components may be radial error components, asymmetric error components, or scan error components. More specifically, the error component may be an asymmetric error component.

In an embodiment, the calculating of a relation between the correction pattern of the representative pattern density and the other pattern density correction map may include selecting a plurality of pattern densities and applying the correction pattern of the representative pattern density to the plurality of pattern density correction maps. The method may include extracting a correction ratio and obtaining a relationship between the correction ratio and the pattern density.

In an embodiment, the selecting of the plurality of pattern densities and extracting the correction ratios for the plurality of pattern density correction maps from the correction pattern of the representative pattern density may be performed by 3σ of the value (B) represented by Equation 1 below. Calculating a value of A to be the minimum;

[Equation 1]

B = T × A-D

Here, T is an asymmetric component of the representative pattern density, D is an asymmetric component of the pattern density to obtain the correction ratio.

In one embodiment, the step of calculating a relation between the correction pattern of the representative pattern density and the other pattern density correction map may include a correction ratio for the asymmetric component correction map of the representative pattern density with the pattern density d as an x-axis variable. And calculating the relational expression with (F) as the y-axis.

Specifically, the relation may be expressed by the following Equation 2.

&Quot; (2) "

F = Ad ² + Bd + C (A, B, C are constants)

In one embodiment, in the step of selecting a representative pattern density for the line width uniformity correction, the line width uniformity may be a line width uniformity of the pattern formed on the photomask.

The present invention can drastically reduce the cost and time required for line width uniformity correction by preparing a correction map for representative pattern density and generalizing it to be applied to all pattern densities.

1 is a flow chart of a line width uniformity correction method according to an embodiment of the present invention.
Figure 2 shows the error of the measured line width.
3 shows the extracted radial error component.
4 shows the extracted asymmetric error component.
5 shows the extracted scan error component.
6 shows radial error components for each pattern density.
7 illustrates asymmetric error components for each pattern density.
FIG. 8 is a diagram illustrating obtaining asymmetry component correction ratios for each pattern density, and FIG. 9 shows a relational expression thereof.
10 shows an example of obtaining a correction map when the pattern density is 2%.
11 shows the overall linewidth uniformity and the linewidth uniformity of the asymmetrical component before and after correction when the pattern density is 2% according to the linewidth uniformity correction method of the present invention.

A pattern to be transferred is formed on the photomask, and the pattern may be formed using electron beam lithography. The pattern is formed in an exposure, development, and etching process, and a critical dimension (CD) may be largely divided into a development inspection CD (DICD) and a final inspection CD (FICD). When the DICD or FICD is measured on the photomask, an error (deviation) of the line width occurs for each photomask position, and the error of the line width includes various error components generated by various causes.

On the other hand, since the line width error can be converted into an error for the line width uniformity, the line width error and the line width uniformity error will be used together below. In other words, the line width correction and the line width uniformity correction can be regarded as substantially the same.

The present invention is particularly effective for correcting line width uniformity of a photomask. There is no limitation on the photomask in which the line width uniformity correction is performed. For example, a Binary Intensity Mask (BIM) may be a Phase Shift Mask (PSM) as well as a strong PSM, a weak PSM, and other masks.

1 is a flow chart of a line width uniformity correction method according to an embodiment of the present invention. As shown in FIG. 1, the line width uniformity correction method of the present invention includes selecting a representative pattern density (S100), creating a correction map of the representative pattern density (S110), and calculating a correction map relation equation (S120). It can be made, including).

(1) Representative Pattern Density Selection Step

In the step of selecting the representative pattern density, the line widths of the plurality of pattern densities are measured, the error components of the line widths are extracted based on the measured line widths, and the correlations between the pattern densities are analyzed for the extracted line width error components. A high error component can be extracted as an error component for correcting the representative pattern density. This will be described in detail below.

To this end, first, the line width is measured for each photomask position to extract the line width error. The error of the extracted line width can be summarized as in the following Table 1. Table 1 shows a 5 × 5 matrix form as an example, but in theory, it can be analyzed in the form of N × N (M, where N is a natural number) matrix.

Table 1 below divides the photomask into 25 parts in a mesh form and measures line widths for each zone, and displays errors for each zone. That is, the average of all the measured line widths is AVG, and when the line widths of row i (i = 1 to 5) and j column (j = A to E) are M _ij , the row i and j columns of Table 1 are as follows. The value to be filled may be M _ij -AVG. For example, A1 in Table 1 may be a value obtained by subtracting the average value AVG from the line width of the area to which row 1 and column A belong. In this case, M _ij may be an average value of a plurality of line widths measured in a region where i rows and j columns intersect.

Figure 2 shows the error of the measured line width. FIG. 2 illustrates an error of a line width including all error components of a line width to be described below. In FIG. 2, the line width is smaller than the average value as the blue color is darker, and the line width is larger than the average value as the red color is darker. It is part. The same applies to the following drawings.

[Table 1]

Next, the error component of the line width is extracted. However, if it is possible to create a correction map applied to all the pattern densities described later in the state where all the error components are included, error component extraction may be omitted. The error components include radial error components, asymmetric error components, scan error components, and the like.

The radial error component may be a component that occurs because the thickness of the photoresist during the lithography process, the temperature of the hotplate in the pre-bake process, and the like change from the center to the edge. For example, a loading error or a fogging error, etc. which appear in the developing process and the etching process may be mentioned. The fogging error is a phenomenon caused by exposing the electron beam resist of an undesired portion that is reflected inside or on the surface of the electron beam resist and under the objective lens of the electron beam irradiator. The radial error component may be extracted as shown in Table 2 below. For example, in Table 2 below, the radial error component (= A1E1A5E5) in row 1 and column A may be defined as an average value of A1, E1, A5, and E5 of Table 1. 3 shows the extracted radial error component.

[Table 2]

Side error components can be extracted as shown in Table 3 below. For example, the asymmetric components in row 1, column A can be defined as the mean values of A1, B1, A2, and B2 in Table 1, and the asymmetric components in row 2, column D are C1, D1, E1, C2, and D2 in Table 1. , E2, C3, D3 and E3 can be defined as the average value. 4 shows the extracted asymmetric error component.

[Table 3]

The scan error component may be an error component related to a developer scan, and may be extracted as shown in Table 4 below. For example, the scan error component of row 1 and column A may be defined as an average value of A1 and B1 in Table 1. 5 shows the extracted scan error component.

[Table 4]

The error component extraction operation of the above-described line width may be performed for each pattern density. That is, for example, radial error components, asymmetric error components, scan error components, and the like of the rare layers having pattern densities of 2%, 10%, 15%, and 25% may be extracted for each pattern density of the photomask. If only the asymmetric error component is to be investigated, only the asymmetric error component may be extracted, and other error components other than the aforementioned error component may be extracted.

The pattern density means the ratio of the area occupied by the pattern to the total area of the photomask. 6 shows radial error components for each pattern density. For example, (A) has a density of 2%, (B) has a density of 10%, (C) has a density of 15%, and (D) has a density of 25. The radial error component in% is shown. 7 shows asymmetric error components for each pattern density. For example, (A) has a density of 2%, (B) has a density of 10%, (C) has a density of 15%, and (D) has a density of 25. Asymmetric error component in case of% is shown. As shown in FIG. 7, it can be seen that the asymmetric error component of the line width, in particular, has a similar tendency regardless of the pattern density.

Next, analyze the correlation by pattern density. That is, correlations between line width uniformity (CDU) (or line width error) of DICD or FICD may be analyzed for each pattern density. Correlation analysis may be performed for each type of linewidth error. That is, correlation for radial error components, correlation for asymmetric error components, or correlation analysis for scan error components may be performed.

Table 5 below shows, as an example, the correlation of radial error components of line width (FICD) (or line width uniformity), and Table 6 analyzes the correlation of asymmetric error components of line width (FICD) (or line width uniformity). Table 7 analyzes the correlation of scan error components to linewidth (FICD) (or linewidth uniformity). The pattern density in Tables 5 to 7 below is arbitrarily selected, and the correlation may be analyzed by other pattern densities. For example, the correlation may be analyzed by any other pattern density, such as 3%, 13%, 17%, but not 2%, 10%, 15%, and 25%.

Radial 2% 10% 15% 25% 2% 1.00 0.69 0.69 0.66 10% 0.69 1.00 0.82 0.84 15% 0.69 0.82 1.00 0.76 25% 0.66 0.84 0.76 1.00

Side 2% 10% 15% 25% 2% 1.00 0.98 0.97 0.94 10% 0.98 1.00 0.98 0.96 15% 0.97 0.98 1.00 0.98 25% 0.94 0.96 0.98 1.00

Row-row 2% 10% 15% 25% 2% 1.00 0.25 0.15 0.14 10% 0.25 1.00 0.12 0.35 15% 0.15 0.12 1.00 0.19 25% 0.14 0.35 0.19 1.00

As shown in Tables 5 to 7, the correlation of the asymmetric error component is 0.94 or more, it can be seen that the error component is very correlated with each other even if the pattern density is different. This can be interpreted to mean that the error of the line width is similar even if the pattern density is different. If the correction map for one pattern density is made, it can be equally applied to the other pattern density. Hereinafter, the description will be made based on the case of correcting the asymmetric error component, but the core idea of the present invention can be applied to the case of correcting other error components.

Next, a representative pattern density for line width (uniformity) correction is selected. For example, it can be seen from Table 6 that the pattern density of 10% is the most representative (highest correlation), and this 10% can be selected as the representative pattern density. In this embodiment, 10% may be selected as the representative pattern density, but in some cases, 2% may be selected, 25% may be selected, and other pattern densities may be selected.

(2) representative pattern density Correction map  Creation steps

A linewidth uniformity correction map for the selected representative pattern density is prepared. The correction map for the representative pattern density may be a correction map for any one or more error components of the line width uniformity of the representative pattern density. If the correlation by pattern density is high for all error components, a representative pattern density may be selected for all the error components and a correction map may be prepared. In addition, if the correlation between line width errors for each pattern density is high without extracting an error component, the error component may not be extracted.

Table 8 below is a correction map of asymmetric components of representative pattern densities. As described above, since the asymmetry error component has a high correlation, it will be described based on this. As an example, Table 8 shows the correction map of the FICD when the pattern density is 10%. In Table 8, R1 to R16 and C1 to C18 are the positions of the photomasks when the photomasks are divided into mesh forms. The value shown in Table 8 may be a CD value to be corrected, or may be a physical quantity required for the CD correction. That is, the two may be converted by a mathematical formula or experimentally, and may be, for example, nm, which is a CD value to be corrected, or may be a dose change amount of an electron beam required for the CD correction, or a dose in which CD correction is reflected. May be the quantity itself.

[Table 8]

(3) Correction map  Relational calculation step

Next, a relationship between the asymmetric component correction map of the representative pattern density and the other pattern density asymmetric component correction map is calculated. To this end, first, a plurality of pattern densities are selected, and a correction ratio (hereinafter, referred to as F) for a representative pattern density correction map of the plurality of pattern density correction maps can be obtained. In other words, it is not practical to find the correction ratios for all the pattern densities, so select a few pattern densities, calculate the correction ratios for the correction maps of the representative pattern densities for each pattern density, and generalize them so that they can be applied to all the pattern densities. Can be rough. Specifically, the A value F at which 3σ (standard deviation) of the value B represented by the following equation (1) is minimized can be calculated.

[Equation 1]

B = T × A-D

Here, T is an asymmetric component of the representative pattern density, and D is an asymmetric component of the pattern density for which the correction ratio is to be obtained.

8 shows an example of obtaining the correction ratio F. As shown in FIG. In FIG. 8, (A) has a pattern density of 2%, (B) has a pattern density of 15%, and (C) has a pattern density of 25%. The correction ratio F obtained in FIG. 8 is shown in Table 9 below. For example, an asymmetric component correction map when the pattern density is 2% means that it can be obtained by multiplying 1.1 by an asymmetric component correction map having a representative pattern density of 10%. The correction ratio F may be expressed as a function of pattern density since the value varies depending on the pattern density.

Pattern density Optimal Ratio (F) 2% 1.1 10% One 15% 0.85 25% 0.7

Next, when the relationship between the pattern density d and the y-axis and the correction ratio F is determined on the x-axis, the relation that can be applied to all the pattern densities can be obtained.

9 shows a graph for obtaining the relational expression. The relationship between F and d shown in FIG. 9 is a quadratic equation and has a relationship of F (d) = -2.193d ² -1.251d + 1.134, and the correlation coefficient R is about 0.98 (R ² = 0.96), which is very high. It can be seen that. The relationship between F and d illustrated in FIG. 9 may be quadratic, linear, or three or more quadratic.

Next, a correction map for each pattern density may be prepared and a line width uniformity may be corrected according to the relationship between F and d. For example, in order to correct the line width uniformity of the pattern is a pattern density of 5% is substituted for the relational expression of the F and 0.05 d (F (0.05) = -2.193 × 0.05 2 - 1.251 × 0.05 + 1.134 ≒ 1.06) of about An F value of 1.06 can be obtained, and a 5% correction map can be obtained by multiplying the 10% correction map, which is a representative pattern density.

10 shows an example of obtaining a correction map when the pattern density is 2%. As shown, a correction map with a pattern density of 2% can be obtained by multiplying the correction map with a pattern density of 10% by 1.1.

11 shows the overall linewidth uniformity and the linewidth uniformity of the asymmetrical component before and after correction when the pattern density is 2% according to the linewidth uniformity correction method of the present invention. In the figure, CDU is the overall line width uniformity, and Side is the line width uniformity of the asymmetric component. As shown, it can be seen that 3σ of the overall line width uniformity was decreased from 2.8 nm to 1.5 nm, and 3σ of the asymmetric component was decreased from 2.7 nm to 0.7 nm. This means that an asymmetric component can be controlled irrespective of the pattern density by preparing a correction map for one representative pattern density and obtaining a correction ratio of each pattern density with respect to the correction map for the representative pattern density.

Meanwhile, the above-described embodiment of the present invention relates to the method for correcting the line width uniformity of the photomask, but the core idea of the present invention can be applied to the line width uniformity correction on the wafer.

Claims (9)

After measuring the line widths for a plurality of pattern densities, extracting a line width error component based on the measured line widths, and analyzing the correlation for each pattern density with respect to the extracted line width error components, representative pattern density for line width uniformity correction Selecting a step;
Creating a correction map for any one or more error components selected from among a radial error component, an asymmetric error component, and a scan error component that are line width uniformity error components with respect to the selected representative pattern density; And
Calculating a relationship between the representative pattern density correction map and another pattern density correction map
Line width uniformity correction method comprising a. delete delete Claim 4 has been abandoned due to the setting registration fee. The method of claim 1,
And generating a correction map for any one or more error components of the selected representative pattern density line width uniformity error components, wherein the error components are asymmetric error components. Claim 5 was abandoned upon payment of a set-up fee. The method of claim 1,
Calculating a relation between the representative pattern density correction map and another pattern density correction map
Selecting a plurality of pattern densities and extracting a correction ratio for the plurality of pattern density correction maps from the representative map density correction map; And
Obtaining a relationship between the correction ratio and the pattern density
Line width uniformity correction method comprising. Claim 6 has been abandoned due to the setting registration fee. The method of claim 5,
The step of selecting the plurality of pattern densities and extracting the correction ratios for the plurality of pattern density correction maps to the correction map of the representative pattern density, wherein A of 3σ of the value (B) represented by Equation 1 is minimized: Line width uniformity correction method comprising the step of calculating a value.
[Equation 1]
B = T × A-D
Here, T is an asymmetric component of the representative pattern density, D is an asymmetric component of the pattern density to obtain the correction ratio. Claim 7 was abandoned upon payment of a set-up fee. The method of claim 5,
Computing the relational expression between the representative pattern density correction map and another pattern density correction map may include a pattern density (d) as an x-axis variable and a correction ratio (F) for the asymmetric component correction map of the representative pattern density. A line width uniformity correction method comprising the step of obtaining the relational expression with respect to the axis. Claim 8 was abandoned when the registration fee was paid. The method of claim 7, wherein
The relationship is a line width uniformity correction method represented by the following equation (2).
&Quot; (2) "
F = Ad ² + Bd + C (A, B, C are constants) Claim 9 has been abandoned due to the setting registration fee. The method of claim 1,
And selecting the representative pattern density for the line width uniformity correction, wherein the line width uniformity is the linewidth uniformity of the pattern formed on the photomask.

Images