JPH0878309A - Measuring method of distortion - Google Patents

Abstract

PURPOSE: To compute distortion with high accuracy without accumulating an error on the measurement of the quantity of the positional displacement of a measuring mark image when the distortion of a projection optical system is evaluated on the basis of a difference method. CONSTITUTION: The pattern of a test reticle is exposed on a wafer (a step 101), second exposure is conducted at a place displaced in the (x) direction on the wafer (a step 103), and third exposure is performed at a place displaced in the (y) direction on the wafer (a step 104). The quantity of the positional displacement of a box-in-box mark image formed by multiple exposure, the difference of distortion, is measured (a step 106), the values of weights wxi j, wyi ,j applied to each difference of distortion are determined (a step 107), and the X component of distortion is obtained by loading addition by using determined weights (a step 108).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a distortion measuring method for a projection optical system, which is mounted on a projection exposure apparatus used for manufacturing a semiconductor device, a liquid crystal display device, a thin film magnetic head or the like in a lithography process. Distortion of projection optical system (magnification error, distortion of projected image, etc.)
It is suitable for application when measuring characteristics.

[0002]

2. Description of the Related Art Conventionally, a reticle (or photomask, etc.) has been used when manufacturing a semiconductor device or the like by a lithography process.
There is used a projection exposure apparatus that exposes a pattern image of (1) on a wafer (or a glass plate or the like) coated with a photoresist via a projection optical system. The allowable range of the imaging characteristics required for the projection optical system of such a projection exposure apparatus is extremely strict. Among the image forming characteristics, the distortion characteristic of the projection optical system (the image forming characteristic including the magnification error and the distortion of the projected image) becomes the best when the projection optical system is incorporated in the projection exposure apparatus. Is adjusted. In recent projection optical systems, it is required to suppress the distortion to about 10 nm or less,
As a measuring method for measuring the distortion characteristics with high resolution and high accuracy, the applicant has proposed a measuring method using a so-called difference method.

A measuring method using the difference method will be described with reference to FIG. In this case, the measurement direction is defined as the X direction, and the measurement points x ₀ (= 0), x ₁ ,
The actual distortion D (x _i ) at x ₂ , ... Is represented by the curve 1 in FIG. 9A. This curve 1
Represents the amount of positional deviation on the wafer (an example of a photosensitive substrate) of the measurement pattern images arranged at a predetermined pitch in the X direction, for example.

Next, by driving the stage on which the wafer is mounted (wafer stage), the wafer is stepped by Δa in the X direction, and then the measurement pattern images are double-exposed on the wafer. Then this 2
Distortion D of the measurement pattern image exposed the second time
(X _i ) is, as indicated by the broken curve 2 in FIG.
The first distortion is moved by Δa in the -X direction. Therefore, after developing the double-exposed wafer, the positional deviation amount of the measurement pattern image is measured using a highly accurate registration measuring machine (coordinate measuring machine). Specifically, as shown in FIG. 9C, at each measurement point x ₀ , x ₁ , x ₂ , ... On the wafer, the measurement pattern image exposed for the first time and the measurement pattern exposed for the second time are measured. A difference ΔD (x _i ) between the position and the pattern image is obtained. This difference ΔD
By multiplying the _{(x i) (Δx / Δa} ), the difference value of the distortion D (x _i) (differential value) d (x _i) is determined.

[0005] Therefore, for example, the origin (x ₀₎ Distortion F (x computational at the measurement point x _i on the basis of the
_i ) (curve 3 in FIG. 9D) is obtained by measuring point x ₀
~x _i until the difference value d a (x _i) may be integrated. That is, the distortion F (x _i ) is expressed as follows, where Σ represents the sum of 0 to i−1 regarding the subscript j.

F (x _i ) = Σd (x _i ) = {ΣΔD (x
_i )} · Δx / Δa By this, the actual distortion D (x _i ) is approximately calculated. In other words, in the measurement method using the difference method, the difference in distortion between adjacent positions in the exposure field of the projection optical system is sequentially obtained, and the distortion from the reference point (for example, the center position of the exposure field) to the measurement position is measured. The difference is integrated, and this integrated value is used as the distortion of the measurement position.

[0007]

As described above, according to the conventional difference method, the amount of positional deviation of the measurement pattern image formed by multiple exposure is measured with high accuracy by a registration measuring machine or the like. Can measure the distortion of the projection optical system with high accuracy. However, since the registration measuring machine and the like actually have a certain degree of measurement error, the measurement result of the positional deviation amount of the measurement pattern image also includes a predetermined measurement error. Therefore, if the difference method is simply applied, the measurement error of the distortion at the measurement point distant from the reference point may exceed the permissible value because, for example, a large number of measurement values are added to the measurement points farther from the reference point. It was

Further, in the difference method, since the wafer stage is driven to step the wafers to perform the multiple exposure, the positioning error of the wafer stage at the time of performing the multiple exposure directly becomes an error with respect to the distortion measurement result.
Therefore, in order to measure the distortion with higher accuracy, it is necessary to reduce the positioning error of the wafer stage.

In view of such a point, the present invention provides a distortion measuring method for calculating the distortion of a projection optical system based on the measurement result of the positional deviation amount of a measurement mark image formed by multiple exposure, and measuring the positional deviation amount. The objective is to calculate distortion with high accuracy without accumulating errors. Further, the present invention drives the positioning stage to shift the position of the photosensitive substrate, multiple-exposes the measurement mark image on the substrate, measures the position shift amount of the measurement mark image, and measures the position shift amount. In the distortion measurement method that calculates the distortion of the projection optical system based on the measurement result of, the distortion is calculated with high accuracy without accumulating the measurement error of the positional deviation amount and by reducing the influence of the positioning error of the stage. The purpose is to do.

[0010]

A distortion measuring method according to the present invention is a distortion measuring method of a projection optical system (13) for projecting an image of a pattern on a first surface onto a second surface. Direction (X direction) and the second direction (Y direction) are formed at equal intervals in the evaluation pattern (27), and the evaluation pattern (27) is at a predetermined interval in the first direction at the first main scale. (28) and the first vernier scale (29) were arranged, and the second main scale (30) and the second vernier scale (31) were arranged at a predetermined interval in the second direction. An evaluation mask (11), which is a mask, is arranged on the first surface of the evaluation mask, and a photosensitive substrate (14) is provided on the second surface
And a pattern image of the evaluation mask (11) is projected onto the substrate (14) through the projection optical system (13).
After the process (step 101), the evaluation mask and the substrate are relatively displaced in the direction corresponding to the first direction by a predetermined distance, an image of the pattern of the evaluation mask is projected onto the projection optical system (13). Second) projecting onto the substrate via
After the step (step 103) and the evaluation mask and the substrate thereof are relatively displaced in the direction corresponding to the second direction by a predetermined distance, an image of the pattern of the evaluation mask is projected by the projection optical system (13). ) To project onto the substrate via
The process (step 104).

Further, the present invention is formed by exposure in the first step and the second step, respectively, at a plurality of positions on the substrate (14) where double exposure is performed in the first step and the second step. Statue of the 1st main scale of Taco (28W)
Fourth step (step 1) for obtaining a measurement value according to the relative positional deviation amount X _{i, j} between the image and the first vernier image (29 W).
06) and a plurality of positions on the substrate (14) where double exposure is performed in the first step and the third step, and second positions formed by the exposure in the first step and the third step, respectively. Of the main scale image (30W) and the second subscale image (31W) of the relative displacement amount Y _{i, j} in the fifth step (step 106), The weights w _{xi, j} and w are respectively added to the measurement values obtained in the fourth step and the fifth step with respect to the measurement point where the distortion should be measured in the measurement direction (X direction) and the reference measurement point. _{yi, j} is given, and a plurality of weights w of the measurement error of the measurement values obtained in the fourth step and the fifth step are provided under the condition that the sum of these plurality of weights becomes a predetermined value (for example, 1). _{xi, j,} w _yi, the weighted square sum is the smallest with _j Plurality of weights w _xi to so _{that, j,} w
The sixth step (step 107) for determining _{yi, j} and the sixth step
Using a plurality of weights w _{xi, j} and w _{yi, j} obtained in the process,
And a seventh step (step 108) for performing the weighted addition of the measurement values obtained in the fourth step and the fifth step to obtain the distortion in the predetermined measurement direction at the measurement point where the distortion should be measured. is there.

In this case, in the fourth step (step 106), the result obtained by subtracting the average value <X _{i, j} > of the positional deviation amounts from each of the relative positional deviation amounts X _{i, j} is obtained. The measured value X ′ _{i, j} is obtained by subtracting the average value <Y _{i, j} > of the positional deviation amounts from each of the relative positional deviation amounts Y _{i, j} in the fifth step (step 106). By using the result Y ′ _{i, j} as the measured value, it is possible to obtain the second or higher-order distortion at the measurement point at which the distortion should be measured in the seventh step (step 108).

Further, in the fourth step (step 106), the result obtained by subtracting the average value and the linear component of the relative displacement amounts X _{i, j} from each of the relative displacement amounts X _{i, j} is the measured value X ″. _{i, j,} and the fifth step (step 1
In 06), the result obtained by subtracting the average value and the linear component of the positional deviation amounts from each of the relative positional deviation amounts Y _{i, j} is set as the measurement value Y ″ _{i, j} . In the step (step 108), the distortion of the third order or higher at the measurement point where the distortion should be measured may be obtained.

Further, with respect to any position other than the measurement point at which the distortion should be measured and the measurement point serving as the reference for the distortion measurement, it was obtained in the fourth step at two positions adjacent to each other in the first direction. The weights given to the measurement values are w _x1 and w _x2 , respectively, and the weights given to the measurement values obtained in the fifth step at two positions adjacent in the second direction are w _y1 and w _y2 , respectively. Then, it is desirable that the condition of the following expression (A1) is satisfied.

−w _x1 + w _x2 + w _y1 −w _y2 = 0 (A1)

[0016]

According to the present invention, the distortion measurement is performed by a method that is a further development of the conventional difference method.
That is, first, as shown in FIG. 6, at each measurement point, the relative position between the main scale image (28W, 30W) and the vernier scale image (29W, 31W) is measured by a registration measuring machine (coordinate measuring machine) or the like. The amount of deviation is measured. After that, in the conventional difference method, since the relative positional deviation amount was added along the predetermined path from the predetermined reference point to the distortion measurement point, the measurement error accumulated as the path became longer. Was there.

On the other hand, in the present invention, when the distortion in the X direction, for example, is obtained at an arbitrary measurement point, the weights w _{xi, j} , X are respectively assigned to the X components of the measurement values obtained in the fourth step and the fifth step. w _{yi, j} is _added . Then, the weight w _{xi, j,} w _yi, the weight so that the sum of the measurement error under the condition that the sum of _j is for example 1 is minimized w _{xi, j,} w _{yi, j}
Is determined, and the X-direction distortion is calculated by performing weighted addition of the X component of each measurement value using these weights w _{xi, j} , w _{yi, j} . Therefore, when calculating the distortion in the X direction at each measurement point, the X component of all measurement values is used with the weights determined so that the total sum of the measurement errors is minimized. The measurement error is not accumulated as much as the measurement point away from.

Further, in the fourth step and the fifth step, when the relative positional deviation amount between the main scale image and the subscale image is used as the measurement value as it is, a normal distortion is required. On the other hand, in the case where the result obtained by subtracting the average value from the measured relative positional deviation amount (registration measurement result) in the fourth step and the fifth step is used as the measurement value, the stage for performing multiple exposure ( The 0th-order component (average value) and the 1st-order component (linear component) of the positioning error of the wafer stage) are completely removed. Further, the magnification error is also removed, and the distortion components of the second or higher order are obtained with high accuracy.

Further, in the fourth step and the fifth step, when the result obtained by subtracting the average value and the linear component from the measured relative displacement amount (registration measurement result) is used as the measurement value, multiple exposure is performed. The 0th-order component and the 2nd-order component of the positioning error of the stage when performing are completely removed. Therefore, a distortion component of the third order or higher is required with high accuracy.

The condition of the expression (A1) is that the distortion at any measurement point is not affected by any value of the distortion at any point other than the measurement point which is the reference for distortion measurement. It means that.

[0021]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the distortion measuring method according to the present invention will be described below with reference to FIGS. The present embodiment is an application of the present invention when measuring the distortion of a projection optical system mounted on a stepper type reduction projection exposure apparatus. FIG. 1 shows a projection exposure apparatus to which the measuring method of this embodiment is applied. In FIG. 1, a reticle 11 on which a transfer circuit pattern is formed is placed on a reticle stage 12, and an illumination optical system not shown is shown. Illumination light IL for exposure from the system (i-line (wavelength 365
nm), KrF excimer laser light (wavelength 248 nm)
Etc.) is irradiated onto the reticle 11. Under the illumination light IL, the pattern on the reticle 11 is reduced and projected onto the photoresist layer on the wafer 14 via the projection optical system 13.
The projection magnification β of the projection optical system 13 is, for example, 1/5.

The wafer 14 is held on the wafer stage through a rotatable wafer table 15.
Here, the Z axis is taken parallel to the optical axis AX of the projection optical system 13, and the X axis is taken parallel to the paper surface of FIG. 2 in a plane perpendicular to the Z axis.
The Y axis is taken perpendicular to the plane of FIG. In this case, the reticle stage 12 adjusts the position of the reticle 11 in the X direction, the Y direction, and the rotation direction (θ direction), and the wafer stage Z adjusts the position of the wafer 14 in the Z direction.
Stage 16, X for positioning the wafer 14 in the X direction
It is composed of a stage 17, a Y stage 18 for positioning the wafer 14 in the Y direction, and the like.

An L-shaped movable mirror 9 for an interferometer is installed on the Z stage 16, and an X-axis interferometer 20 and a Y-axis interferometer (not shown) and the movable mirror 9 are used. , The X and Y coordinates of the Z stage 16 are always 0.01 μm, for example.
Is monitored with high resolution. In accordance with the result of monitoring in this way, the X stage 17 is moved by the feed screw 24.
Is driven by the drive motor 23 via the Y stage 1
8 is driven by a drive motor 21 via a feed screw 22. A stage coordinate system (X, Y) is a coordinate system composed of X coordinates and Y coordinates monitored by the X-axis interferometer 20 and the Y-axis interferometer, respectively.

Further, a light transmitting system 25 and a light receiving system 26 of an autofocus system are arranged on the side surface of the projection optical system 13, and the light beam emitted from the light transmitting system 25 is directed to the optical axis AX of the projection optical system 13. The light is obliquely focused on the surface of the wafer 14, and, for example, a slit image is projected on the surface. Then, the reflected light from the slit image is condensed in the light receiving system 26, the slit image is re-imaged on the light receiving element in the light receiving system 26, and the lateral deviation amount of the slit image is obtained from the light receiving element. Focus signal is output. The surface of the wafer 14 is Z
When displaced in the direction, the lateral shift amount of the slit image re-formed in the light receiving system 26 changes. Therefore, calibration is performed in advance so that the focus signal becomes a predetermined reference value when the surface of the wafer 14 matches the image forming surface of the projection optical system 13, and thereafter, the focus signal is adjusted to that value. By driving the Z stage 16 so that it becomes the reference value, autofocusing is performed.

Next, an example of a method for measuring the distortion of the projection optical system 13 in this embodiment will be described with reference to the flowchart of FIG. In this case, the projection optical system 1
The exposure field of 3 is a 20 mm × 20 mm square, and 11 rows × 2 mm are arranged on the exposure field at intervals of 2 mm.
It is assumed that the distortion at each measurement point arranged in a matrix of 11 columns is measured.

FIG. 7 (a) shows a 1 on the exposure field.
The matrix-shaped measurement points of 1 row × 11 columns are shown in FIG.
In (a), each measurement point is represented by P _{i, j} (i = 1 to 1)
1, j = 1 to 11), the distortion at each measurement point is D
_{Expressed as i, j} . Further, the X component and the Y component of this distortion D _{i, j} are represented by (Dx _{i, j} , Dy _{i, j} ). To measure the distortion, a test reticle on which a predetermined evaluation mark is formed is used.

FIG. 3 shows the test reticle 11T used in this embodiment. For the sake of clarity, FIG. 3 shows the test reticle 11T projected onto the wafer 14 via the projection optical system 13 of FIG. Represents the pattern arrangement.
That is, in the pattern area in the light-shielding band 40 of the test reticle 11T, the difference pattern units 27 as the marks for evaluation are arranged in a matrix of 11 rows × 11 columns. The distance between the difference pattern units 27 in the X and Y directions is 2 mm when projected onto the wafer.

FIG. 4 shows the detailed structure of the difference pattern unit 27. In FIG. 4, the difference pattern unit 27 has an outer box mark 28 as a main scale.
And the inner box mark 29 as a vernier is formed at an interval d in the X direction, and the outer box mark 30 as a main scale and the inner box mark 31 as a vernier scale are Y.
It is formed at intervals d in the direction. The inner box marks 29 and 31 are the outer box marks 28 and 30, respectively.
It fits inside the. In this case, the box marks 28 and 29 are marks for measuring the positional deviation of the differential pattern unit 27 when the wafer stage is exposed by stepping the wafer stage in the X direction.
Marks 0 and 31 are marks for measuring the positional deviation of the differential pattern unit 27 when the wafer stage is exposed by stepping in the Y direction.

Next, in step 101 of FIG. 1, the test reticle 11T of FIG. 3 is replaced with the reticle stage 1 of FIG.
In the state where the test reticle 11T is placed on the wafer 2, the pattern image of the test reticle 11T is collectively exposed on the wafer 14 through the projection optical system 13. Next, in step 102, the wafer 14
The test reticle 11T is successively exposed at a pitch Px in the X direction and at a pitch Py in the Y direction. The pitches Px and Py are set to be larger than 20 mm, respectively.

As a result, as shown in FIG.
The pattern images of the test reticle 11T shown in FIG. 3 are exposed on the upper shot areas 32A to 32F, respectively. here,
A wafer coordinate system (x, y) is set on the wafer 14 parallel to the stage coordinate system (X, Y), and the coordinates of the center of the first exposed shot area 32A in the wafer coordinate system (x, y) are set to ( x ₀ , y ₀ ). In this case, the wafer coordinate system (x, y) at the center of the shot areas 32A to 32F of the wafer 14
The coordinates at are (x ₀ + N · Px, y ₀ + M · Py). The range of integer N is 0 to 2, and the range of integer M is 0 or 1.

Next, in step 103, the wafer 1
The pattern images of the test reticle 11T of FIG. This is called "X exposure", and as a result, the center coordinates on the wafer coordinate system are (x ₀ + Δx + N · Px, y ₀ + M · Py), respectively, as shown in FIG.
The pattern images of the test reticle 11T are exposed on the shot areas 33A to 33F represented by.

Next, in step 104, the wafer 1
The pattern image of the test reticle 11T shown in FIG. This is called "Y exposure", and as a result, as shown in FIG. 5, the center coordinates are (x ₀ + N · Px, y ₀ + Δy + M · Py) on the wafer coordinate system.
The pattern images of the test reticle 11T are exposed on the shot areas 34A to 34F represented by.

The positional deviation amount Δx in the x direction and the positional deviation amount Δy in the y direction at this time are commonly expressed by the following equation. Δx = Δy = 2 + d [mm] That is, the positional deviation amounts Δx and Δy are common to the box marks 28, 30 and the box marks of FIG. 4 at the interval (2 mm) between the differential pattern units 27 in the test reticle 11T of FIG. The distance d between 29 and 31 is added.

Next, in step 105 of FIG. 1, the wafer 14 after triple exposure is developed. As a result, FIG.
In the measurement area 35 (i, j) on the wafer 14 corresponding to each measurement point P _{i, j} in FIG.
In-box mark images 36 and 37 are formed. In FIG. 6, in the measurement area 35 (i, j), a box-in-box mark image 37 in which the images 28W and 29W of the X direction box marks 28 and 29 overlap each other and a Y direction box mark 30 are shown. , 31 are overlapped with each other, a box-in-box mark image 36 is formed.

However, in reality, the wafer 1 is not exposed in the first exposure.
Among the images of the difference pattern unit 27 of 11 rows × 11 columns formed in the shot areas 32A to 32F on the No. 4, the box-in-box mark image 37 is formed by the X exposure shifted by Δx in the x direction. Is 2 columns to 11 in each row
It is a difference pattern unit of 11 rows × 10 columns up to a column. Similarly, the Y-exposure shifted by Δy in the y direction forms the box-in-box mark image 36 in the difference pattern unit of 10 rows × 11 columns, which is each column of 1 row to 10 rows.

Next, in step 106, an image outside the box-in-box mark image 37 is measured in each measurement region 35 (i, j) by using a high-precision registration version measuring machine (coordinate measuring machine). The amount of positional deviation X _{i, j} between the 28 W and the inner image 29 W in the X and Y directions,
The positional shift amounts Y _{i, j in} the X direction and the Y direction between the image 30W on the outer side and the image 31W on the inner side of the in-box mark image 36 are measured. The positional displacement amounts X _{i, j} and Y _{i, j} are vectors. In this case, the positional deviation amount X _{i, j} of the box-in-box mark image 37 formed by X exposure is
A box-in-box formed by Y exposure, which represents the difference between the distortions (vectors) D _{i, j + 1} , D _{i, j} of two adjacent measurement points on the left and right (in the X direction of FIG. 7A). The positional deviation amount Y _{i, j} of the mark image 36 is the difference between the distortions (vectors) D _{i, j} , D _{i + 1, j} of two vertically adjacent (Y direction in FIG. 7A) measurement points. It represents. Therefore, the following relationship is established.

X _{i, j} = D _{i, j + 1} −D _{i, j} , Y _{i, j} = D _{i, j} −D _{i + 1, j} Next, at step 107, each of FIG. The X component of the distortion at the measurement point P _{i, j} is obtained. Specifically, for example, the measurement point P _6,6 is used as a reference point (position where the distortion is 0), and the distortion at the measurement point P _6,7 adjacent to the right is obtained. The distortion at the measurement point P _6,7 is from the measurement point P _6,6 to the measurement point P _6,7.
Total distortion difference X _{i, j} , Y in any path up to
_It can be obtained by adding _{i, j} . In this case, there is not only one route, but many routes.

FIG. 7B shows measurement points P _6,6 to measurement point P.
Two paths 38 and 39 up to _6,7 are shown. The distortion differences X _{i, j} and Y _{i, j} are obtained by the registration measuring machine or the like as described above, but the measured value at that time naturally includes a predetermined measurement error, and therefore the distortion difference to be added is calculated. The larger the number, the larger the error in the required distortion value. Therefore, in the conventional difference method, for example, the distortion is calculated with a small measurement error by adding the distortion difference along the shortest path.

On the other hand, in the present embodiment, a plurality of distortion values are obtained by using a plurality of paths, and the weighted averages thereof are well calculated, so that the distortion value is calculated only by the shortest one path. The distortion value can be obtained with a small measurement error. The method of calculating the distortion in this embodiment will be described below.

Also in this embodiment, in FIG. 7A _, the X component Dx _{i, j} of the distortion D _{i, j} at another arbitrary measurement point P _{i, j} is taken with reference to the measurement point P _6,6. Ask for. The above-mentioned distortion difference X _{i, j} is 110 vector quantities from X _{1,1 to} X _11,10 , and the distortion difference Y
_{i, j} are 110 vector quantities Y _1,1 to Y _10,11 . Then, the distortion D at the measurement point P _{i, j
In} order to obtain the X component Dx _{i, j} of _{i, j} , a total of 220 distortion difference vectors X _{i, j} and Y are obtained.
_i, of the _j, each X components X _{xi, j} and Y _{xi, j} only use.

In addition, in the following calculation, a total of 22
Each component of the vector quantity of 0 distortion difference is
Are assumed to include the same error (measurement error) σ
It First, the distortion difference X_{i, j}X component of_{xk, m}To
On the other hand, the weight w_{xk, m}And the distortion
Difference Y_{i, j}X component of Y_{xk, m}For each w
_{yk, m}Is added to the measurement point P_{i, j}Distortion D
_{i, j}X component of Dx_{i, j}Is expressed by the following weighted addition (Equation 1)
You However, the weight w_{xk, m}, And w_{yk, m}Is the sum of all 1
Is standardized as follows. Furthermore, the required distro
X component of solution Dx _{i, j}Total error amount included in_{i, j}To
It is expressed by the following (Equation 2).

[0042]

[Equation 1]

[0043]

[Equation 2]

Then, the square error ε of the total error amount of (Equation 2)
_{i, j} ²Weight w to minimize_{xi, j}, W_{yi, j}Ask for all
It Where weight w_{xi, j}, W_{yi, j}Must be satisfied
Give no conditions. The premise in this case is the measurement point P_{i, j}of
Distortion is at measurement point P_6,6Except for all points
Whatever the impact value,
It means that it should not be received. Obedience
Any measurement point P _{k, m}In each measurement,
Distortion difference X between points_{xk, m-1}, X_{xk, m},
Y_{xk-1, m}, Y_{xk, m}Weight w on_{xk, m-1}, W_{xk, m}, W
_{yk-1, m}, W_{yk, m}Must satisfy the following conditions
Given by the formula.

[0045]

## _EQU00003 ## −w _{xk, m−1} + w _{xk, m} + w _{yk-1, m} −w _{yk, m} = 0 However, the measurement point P _{k, m} is in the peripheral portion, and the distortion difference adjacent to one side is If not (not measured), 0 is substituted for the weight. In addition, the measurement point P
_{When k, m} is the reference measurement point P _6,6 , the condition corresponding to (Equation 3) is as follows.

[0046]

[ _{Mathematical formula-see original document} ] -w _{xk, m-1} + w _{xk, m} + w _{yk-1, m} -w _{yk, m} = 1 Further, the measurement point P _{k, m} is the measurement point P _{i, j} as the distortion measurement target. In some cases, the condition corresponding to (Equation 3) is as follows.

[0047]

[ _Expression 5] −w _{xk, m−1} + w _{xk, m} + w _{yk-1, m} −w _{yk, m} = −1 These conditional expressions (Equation 3) to (Equation 5) are equal to the number of measurement points. 121 is obtained, one of which is automatically determined from the other 120 conditional expressions. Therefore, by eliminating the weights w _{xk, m} and w _{yk, m} in (Equation 2) from 120 independent conditional expressions (Equation 3) to (Equation 5), (Equation 2) becomes 100 ( = 220-120) weights w
It is converted into the following equation consisting of _{xk, m} and _{wyk, m} .

[0048]

(Equation 6)

In this (Equation 6), the constant A (k, m,
k ', m') is a number determined according to the subscripts k, m, k ', m', and the subscripts k, k 'are integers each having a value from 1 to 11, and the subscripts m, m' Are 1 to 1 respectively
It is an integer that takes a value up to 0. In order to obtain the weights w _{xk, m} and w _{yk, m} that minimize the square ε _i ² of the total error amount of ( _Equation 6),
It _suffices to solve 100 simultaneous equations, where 0 is the result of partial differentiation of ( _Equation 6) with 100 weights w _{xk, m} and w _{yk, m} . As a result, 100 weights w _{xk , m} , w
The value of _{yk, m} is obtained. By substituting these into (Equation 3) to (Equation 5), the remaining 120 weights w _{xk, m} , w
The value of _{yk, m} is obtained.

Next, in step 108 of FIG. 1, the decision is made.
220 fixed weights w_{xk, m}, W _{yk, m}In place of (Equation 1)
Enter and measure point P by weighted average_{i, j}Distortion in
D_{i, j}X component of Dx_{i, j}Ask for. Similarly,
Measurement point P_{i, j}Distortion D
_{i, j}Y component of Dy_{i, j}Ask for. Next, step 110
In the same way, the distortion at other measurement points is similarly obtained.
Meru.

11 rows × 11 shown in FIG. 7A of this embodiment.
At the matrix measurement point of the row, the central measurement point P
_{When 6} , ₆ are used as a reference, the distortion error calculated in step 108 of FIG. 1 for the outermost measurement point P _1,1 is 1.37σ from (Equation 2), that is, the measurement error σ of the registration measuring machine. It is known to be 1.37 times. On the other hand, when the conventional difference method is applied to calculate the distortion at the outermost measurement point P _1,1 using only one shortest path, the error is 3.
16 times. Therefore, it can be seen that the method of the present embodiment has a measurement error of 1/2 or less as compared with the conventional difference method.

Next, a second embodiment of the present invention will be described. The second embodiment is exactly the same as the first embodiment until the 220 vector quantities X _{i, j} , Y _{i, j} of the distortion difference are obtained (up to step 106 in FIG. 1). After that, in this embodiment, the calculated 220 vector vectors of the distortion difference are set to the distortion difference X _1,1.
To X _{11, 10} X component _{X x1,1} ~X x11,10, their Y components _X y1,1 ~X y11,10, distortion difference Y _{1, 1} to Y
_{10, 11} of the X component _{Y x1,1} ~Y x10,11, and grouped into four of those Y components _Y y1,1 ~Y y10,11, average every four groups <X _{xi, j} >, <X _{yi, j} >, <Y _{xi, j} >,
<Y _{yi, j} > is calculated. Then, the corresponding average value is subtracted from the value of each group to obtain four new groups X ′ _{x1,1 to} X ′ _x11,10 , X ′ _{y1,1 to} X ′ _y11,10 , Y ′.
_{x1,1 ~Y 'x10,11, Y' y1,1} ~Y 'y10, seeking _11. This is a zero-order component removal process.

After that, using the values of the four new groups, each weight is determined so that the square of the total error amount of (Equation 2) is minimized, as in step 107 and after in the first embodiment. , Distortion is calculated from (Equation 1) using the determined weight. However, in (Equation 1) in this case, the distortion difference components X _{xk, m} and Y _{xk, m} are replaced with new components X ′ _{xk, m} and Y ′ _{xk, m} , respectively. The the obtained distortion in the second embodiment, the difference amount has been subjected to zero-order component removal process _{X 'xk, m, Y'} xk, because it is determined from _m, 1 order component, for example components of magnification such as Is the second or higher order distortion removed. Also,
If the wafer stage in FIG. 2 has a predetermined positioning error, X exposure in step 103 or Y in step 104 in FIG.
Even if a positioning error occurs during exposure, the offset component of the positioning error and the component that simply changes in proportion to the position in the X and Y directions are removed in the second embodiment.

Next, a third embodiment of the present invention will be described. Also in this third embodiment, the same process as in the first embodiment is performed until 220 distortion difference vector amounts X _{i, j} , Y _{i, j} are obtained (up to step 106 in FIG. 1). After that, in this embodiment, the calculated 220 vector vectors of the distortion difference are set to the distortion difference X _1,1.
To X _{11, 10} X component _{X x1,1} ~X x11,10, their Y components _X y1,1 ~X y11,10, distortion difference Y _{1, 1} to Y
_{10, 11} of the X component _{Y x1,1} ~Y x10,11, and grouped into four of those Y components _Y y1,1 ~Y y10,11, average every four groups <X _{xi, j} >, <X _{yi, j} >, <Y _{xi, j} >,
<Y _{yi, j} > and a linear component are obtained. The linear component is X
The error component is caused by a magnification error (scaling) in the direction, a scaling in the Y direction, a minute rotation error, and a minute orthogonality error between the X axis and the Y axis.

To specifically obtain the linear component, FIG.
Distortion difference X _{6, 6} stage coordinate system in (a) (X, Y) as the coordinates of above, the measuring points P _6,6 and P
Take the midpoint coordinates of the _6,7, as well as other distortion difference X _{i, j,} Y _i, also uses two coordinates of the midpoint of the measurement point taking the difference as the coordinates of the _j. Then, the function for obtaining the corresponding distortion difference vector from the coordinates in the stage coordinate system (X, Y) is represented by a conversion matrix of 2 rows × 2 columns and an offset matrix of 2 rows × 1 column, and the least squares law is used. Then, four parameters (scaling in the X direction, scaling in the Y direction, rotation, orthogonality) forming the elements of the conversion matrix and two offsets forming the offset matrix are obtained. After that, the residual component obtained by subtracting the distortion difference calculated using the conversion matrix and the offset matrix from the actually measured distortion difference is the result of removing the average value and the linear component.

In this way, by subtracting the corresponding mean value and linear component from the distortion difference values of each group, four new groups X " _x1,1 ...
X " _x11,10 , X" _y1,1 ~ X " _y11,10 , Y" _x1,1 ~ Y "
_x10,11, seek _Y "y1,1 ~Y" y10,11. This can be said to be a primary component removal process. After that, by using the values of the four new groups, each weight is determined so that the square of the total error amount of (Equation 2) is minimized, as in step 107 and subsequent steps of the first embodiment, and then determined. Distortion is calculated from (Equation 1) using the weights. However, in this case (Equation 1), the distortion difference component X
_{xk, m} and Y _{xk, m} are new components X ″ _{xk, m} and Y ″ _{xk, m, respectively.}
Has been replaced by. The distortion obtained in the third embodiment is obtained from the difference amounts X ″ _{xk, m} and Y ″ _{xk , m} that have been subjected to the first-order component removal process, and therefore the first-order component and the second-order component are It is distortion not less than 3rd order. As in the second embodiment, the wafer stage of FIG. 2 has a predetermined positioning error, and step 103 of FIG.
Even if the positioning error occurs in the X exposure of 1 or the Y exposure of step 104, the offset component, the linear component, and the quadratic component (the component represented by the square of the position) of the positioning error are generated in the third embodiment. To be removed.

Next, referring to FIG. 8 for the fourth embodiment of the present invention.
I will explain. In this example, for easy understanding,
Measurement point P of 11 rows × 11 columns as in 7 (a)_1,1~ P
_11,11Instead of using
Measurement point P of 3 rows x 3 columns_1,1~ P _3,3Handle if there is.
In this case, the center measurement point P_2,2Is the origin O (reference point)
Then, the distortion at the origin O is regarded as 0. So
Then, around it, it may be an ideal lattice point due to distortion.
8 measurement points P that are slightly shifted from_1,1~ P_3,3Is the first
Measurement point P in one row _1,1~ P_3,1And in the second row offset in the X direction
Measuring point P_1,2~ P_3,2The difference in distortion with
Re X₁, X₃, X_FiveAnd the measurement point P in the second row_1,2~ P
_3,2And the measurement point P in the third row that is offset in the X direction_1,3~ P_3,3When
Distortion difference of X ₂, X_Four, X₆Tosu
It Similarly, the measurement point P on the first row_1,1~ P_1,3 And in the Y direction
Deviated measurement point P of the second row_2,1~ P_2,3Distortion with
Each difference is Y₁, Y₂, Y₃And measure the second line
Point P_2,1~ P_2,3And the measurement point P on the third row that is displaced in the Y direction
_3,1~ P_3,3And the distortion difference with Y_Four,
Y_Five, Y₆And

At this time, assuming that the distortion differences each include a measurement error (standard deviation) σ, the vector amount D _2,3 of the distortion (deviation amount from the ideal grid point) at the measurement point P _2,3 is totaled. Obtained under the condition that the amount of error is minimized. Distortion D with conventional difference method
There are various routes to obtain ₂ and _3, and the error will differ depending on the route taken. For example, if a path is taken straight from the origin O in the + X direction to the measurement point P _2,3 , D _2,3 =
X ₄ and error = σ, and if a path from the origin O to the measurement points P _1,2 and P _1,3 to the measurement point P _2,3 is taken,
D _2,3 == q ₂ + p ₂ -q ₃ , and the error is 3 ^1/2 σ.

[0059] In addition, further improved accuracy when weighted average both at 1 / (error) ² _{weight, D 2, 3 = (3p} 4 + q 2
+ P ₂ −q ₃ ) / 4, error = (3/4) ^1/2 σ.
If you do the same calculation using all possible routes,
The distortion D _2,3 can be obtained with the minimum error. Such calculation is not so difficult if it is 3 rows × 3 columns, but the labor is immeasurable when the number of measurement points increases. Therefore, weights w ₁ to w ₁₂ are given to the respective distortion differences X _{1 to} X ₆ and Y _{1 to} Y ₆ as follows, and the distortions D ₂ and ₃ are weighted as follows in correspondence with (Equation 1). Expressed by addition.

[0060]

[Formula 7] D _2,3 = w ₁ · X ₁ + …… + w ₆ · X ₆ + w ₇ · Y ₁ + …… + w ₁₂ · Y ₆ At this time, the total error amount ε ₂ corresponding to (Formula 2) The square of ₃ is expressed by the following equation.

[0061]

(8) ε_2,3 ²= (W₁ ²＋ …… ＋ w₆ ²+ W₇ ²＋ …… ＋ w₁₂ ² ) ・ Σ²  This total error amount ε_2,3So that w is minimized₁~ W₁₂
Should be decided. These weights w₁~ W₁₂Each is German
It cannot be decided vertically. For example, the measurement point P _1,1To arrive
Looking at it, the distortion difference X₁Is the measurement point P_1,1
Distortion from the ideal lattice point of_1,1And measurement point P
_1,2Distortion D_1,2Difference with
Difference Y₁Is the measurement point P_1,1Distortion D_1,1When
Measuring point P _2,1Distortion D_2,1Is the difference between
It Therefore, distortion D_{1, 1}Depending on the size of
Distortion difference X₁, Y₁Since the value of changes,
Distortion to be D_2,3Dist unrelated to
Option D_1,1In order not to be affected by the size of
w₁And w₇Must have the same value. That is, (number
The following condition corresponding to 3) must be satisfied.

Regarding measurement point P _1,1 : + w ₁ −w ₇ = 0 For the remaining 8 measurement points, the following conditions must be satisfied corresponding to (Equation 3) to (Equation 5). Regarding the measurement point P _1,2 : −w ₁ + w ₂ −w ₈ = 0, regarding the measurement point P _1,3 : −w ₂ −w ₉ = 0, regarding the measurement point P _2,1 : + w ₃ + w ₇ −w ₁₀ = 0, with respect to the origin O: −w ₃ + w ₄ + w ₈ −w ₁₁ = 1, with respect to the measurement point P _2,3 : −w ₄ + w ₉ −w ₁₂ = −1, with respect to the measurement point P _3,1 : + w ₅ + w ₁₀ = 0, with respect to the measurement point P _3,2 : -w ₅ + w ₆ + w ₁₁ = 0, with respect to the measurement point P _3,3 : -w ₆ + w ₁₂ = 0

By summarizing the above, the following (Equation 9) is obtained.

[0064]

[Equation 9]

From this, the eight weights in the twelve weights w _{1 to} w ₁₂ can be eliminated. That is, eight weights w _{1 to} w ₇ , w
₁₀ is expressed by the following equation using the remaining four weights w ₈ , W ₉ , w ₁₁ , and w ₁₂ .

[0066]

[Equation 10]

Although there are nine conditional expressions relating to weights, only eight weights can be deleted as shown in (Equation 10).
This is because if the eight conditional expressions relating to the weights are determined, the remaining one conditional expression is automatically determined. Substituting (Equation 10) into (Equation 8), the total error amount ε _2,3 becomes 4 as follows.
The individual weights are represented by w ₈ , w ₉ , w ₁₁ , and w ₁₂ , and these four weights can be selected independently of each other. This (Equation 1
1) is an expression corresponding to (Equation 6).

[0068]

[Equation 11] ε _2,3 ² = (4w ₈ ² + 6w ₉ ² + 4w ₁₁ ² + 6w
₁₂ ² + 6w ₈ · w ₉ −2w ₉ · w ₁₁ + 6w ₁₁ · w ₁₂ −2
_{w 12 · w 8 -2w 8 ·} w 11 -4w 9 · w 12 + 2w 9 -2
w ₁₂ ) · σ ^{2 In} order to obtain the weights w ₈ , w ₉ , w ₁₁ , and w ₁₂ so that the square of this total error ε _2,3 ² is minimized, the result of differentiating (Equation 11) is obtained. It suffices to solve the following equation, which is four simultaneous equations obtained by setting 0 as 0.

[0069]

[Equation 12]

By substituting the four weights w ₈ , w ₉ , w ₁₁ , and w ₁₂ obtained from this (Equation ₁₂ ) into (Equation 10), all the weights are determined as follows.

[0071]

[Equation 13]

Substituting these weights into (Equation 7) and (Equation 8), the squares of the distortion D _2,3 and the total error amount ε _2,3 to be obtained are as follows.

[0073]

[Equation 14] D _2,3 = (p ₁ + 5p ₂ -2p ₃ + 14p <sub>4
+ P 5 + 5p 6 + q</sub> 1 + 4q 2 -5q 3 -q 4 -4q 5
+ 5q ₆ ) / 24

[0074]

## EQU15 ## ε _2,3 ² = (7/12) σ ² Therefore, the total error amount ε _2,3 is as follows.

[0075]

[Equation 16] ε _2,3 = (7/12) ^1/2 · σ By expanding the above method, the distortion when the total error amount becomes minimum even if the number of measurement points increases, and the distortion at that time The total amount of error can be calculated. by the way,
The difference method of each of the above-described embodiments can be replaced with an electric circuit model. For example, the measurement point P _{i, j} shown in FIG. Is regarded as an electric circuit, and it is considered that there is a predetermined resistance between each measurement point. At this time, when the reference point is P _6,6 , the measurement target point is P _6,7 , and a voltage is applied between the reference point and the measurement target point, the current flowing between these two points causes power consumption of the entire system. It flows so that P becomes the minimum. The specifications in the electric circuit model at this time correspond to the specifications in the difference method of the above-described embodiment as follows.

Resistance value between measurement points → square of error of difference in distortion between measurement points (σ ² ), current i flowing through one side between measurement points when unit current is flown between two points → weights _{w xk, m, w yk,} m, power consumption P / I of the entire system per unit current, i.e. the entire system of the squares of the total resistance R → total error amount (ε _6,7 ²⁾

In the above embodiment, the box-in-box mark is used as the main scale and the sub-scale, but other than the main scale and the sub-scale, for example, a cross pattern, a line-and-space pattern, etc. May be used. Further, it is also possible to use a mark or the like which can apply the principle of moire fringes to enlarge the relative positional deviation amount. Further, one cross mark or the like may be used for both the main scale and the sub scale. In this case, an offset that exceeds the maximum distortion is added to the lateral shift amount in the X direction, so that the first exposed mark and the next exposed mark can be distinguished.

As described above, the present invention is not limited to the above-described embodiments, and various configurations can be adopted without departing from the gist of the present invention.

[0079]

According to the present invention, when the distortion at an arbitrary measurement point is obtained, the sum of the measurement error of the relative positional deviation amount between the main scale image and the subscale image is determined to be the minimum. Since the distortion is obtained by weighted addition of all the positional deviation amounts using the weights, the measurement error of the registration measuring machine etc. at the time of measuring the positional deviation amounts does not accumulate, and it is highly accurate. There is an advantage that the distortion can be calculated.

Incidentally, when the distortion measurement points are distributed in the grid points of 11 rows × 11 columns, the total error when the distortion at the measurement point in the upper right corner is obtained by the method of the present invention with the central measurement point as a reference. The amount is 1.37 times the measurement error σ of the registration measuring machine or the like. On the other hand, when the conventional difference method is applied to calculate the distortion along, for example, one shortest path, the total error amount is 3.16 times the measurement error σ. Therefore, in the calculation method according to the present invention, the total error amount becomes half or less.

The weighted addition processing described above is applied to the result obtained by subtracting the average value from the relative positional deviation amount, so that the 0th-order and 1st-order positioning errors of the stage position at the time of multiple exposure are The influence and the influence of the magnification error of the projection optical system are eliminated, and the second or higher order distortion is required. Further, by performing the above-described weighted addition processing on the result of subtracting the average value and the linear component from the relative positional deviation amount, the 0th-order, 1st-order and 2nd-order Effect of positioning error,
In addition, the influence of the magnification error of the projection optical system is eliminated, and the distortion of the third order or higher is required.

Further, the value of the weight can be accurately determined by imposing the condition of the expression (A1) on the weight.

[Brief description of drawings]

FIG. 1 is a first distortion measuring method according to the present invention.
It is a flow chart which shows an example.

FIG. 2 is a schematic configuration diagram showing a projection exposure apparatus in which the distortion measuring method of the embodiment is implemented.

FIG. 3 is a plan view showing a pattern arrangement in a state where a test reticle used in an example is projected on a wafer.

FIG. 4 is an enlarged plan view showing a pattern arrangement of a differential pattern unit 27 in FIG.

FIG. 5 is a plan view showing a shot array on the surface of the wafer 14 after triple exposure is performed in the example.

6 is an enlarged plan view showing a configuration of box-in-box mark images 36 and 37 in a measurement area 35 (i, j) in FIG.

FIG. 7A is a diagram showing a state in which the exposure field of the projection optical system to be measured is divided into 11 rows × 11 columns of measurement points;
FIG. 7B is an enlarged view showing a part of FIG. 7A.

FIG. 8 is a diagram showing a state in which an exposure field to be measured is divided at measurement points of 3 rows × 3 columns.

FIG. 9 is a diagram for explaining a procedure for obtaining distortion by a conventional difference method.

[Explanation of symbols]

11T test reticle 12 reticle stage 13 projection optical system 14 wafer 15 wafer table 16 Z stage 17 X stage 18 Y stage 20 interferometers 21 and 23 drive motor 25 autofocus light-transmitting system 26 autofocus light-receiving system 27 differential pattern Unit 28,30 Outside box mark 29,31 Inside box mark 35 (i, j) Measuring area 36,37 Box-in-box mark image P _{1,1 to} P _11,11 Measuring points

Claims (4)

[Claims] 1. A method for measuring distortion of a projection optical system for projecting an image of a pattern on a first surface onto a second surface, wherein an evaluation pattern is provided at equal intervals in a first direction and a second direction which are different from each other. And a first main scale and a first sub-scale are arranged at a predetermined interval in the first direction, and the evaluation pattern has a second main scale at a predetermined interval in the second direction. And a second sub-scale are arranged, an evaluation mask is arranged on the first surface, a photosensitive substrate is arranged on the second surface, and an image of the pattern of the evaluation mask is arranged. A first step of projecting light onto the substrate via the projection optical system;
After relatively shifting the evaluation mask and the substrate by a predetermined distance in the direction corresponding to the first direction, an image of the pattern of the evaluation mask is projected onto the substrate via the projection optical system. A second step of: shifting the evaluation mask and the substrate relative to each other in a direction corresponding to the second direction by a predetermined distance, and then forming an image of the pattern of the evaluation mask through the projection optical system. A third step of projecting onto the substrate by means of the above; at each of a plurality of positions on the substrate where double exposure was performed in the first step and the second step, the first step
The first formed by the exposure in the step and the second step
A fourth step of obtaining a measurement value according to a relative positional deviation amount between the main scale image and the first subscale image; and double exposure in the first step and the third step on the substrate. At each of a plurality of positions where the second main scale image and the second main scale image formed by the exposure in the first step and the third step are formed.
A fifth step of obtaining a measurement value according to a relative displacement amount with respect to the image of the vernier scale; With respect to the measurement point, the plurality of measurement values obtained in the fourth step and the fifth step are respectively weighted, and under the condition that the sum of the plurality of weights becomes a predetermined value, the fourth step and A sixth step of determining the plurality of weights so that the weighted square addition result using the plurality of weights of the measurement error of the measurement value obtained in the fifth step is minimized;
Using the plurality of weights obtained in the sixth step, the fourth
And the seventh step of obtaining the distortion in the predetermined measurement direction at the measurement point where the distortion should be measured by performing weighted addition of the measurement values obtained in the step and the fifth step. . 2. In the fourth step, a result obtained by subtracting an average value of the plurality of relative positional deviation amounts from each of the relative positional deviation amounts is set as the measurement value, and the fifth step is performed. In the measurement, the result obtained by subtracting the average value of the plurality of relative displacement amounts from each of the relative displacement amounts is the measurement value, and the distortion should be measured in the seventh step. The distortion measuring method according to claim 1, wherein a distortion of second or higher order is obtained at each point. 3. A result obtained in the fourth step by subtracting an average value and a linear component of the plurality of relative positional deviation amounts from each of the relative positional deviation amounts is set as the measurement value, In the fifth step, the measurement value is a result obtained by subtracting the average value and the linear component of the plurality of relative positional deviation amounts from each of the relative positional deviation amounts, and in the seventh step, The distortion measuring method according to claim 1, wherein a distortion of a third order or higher at a measurement point where the distortion is to be measured is obtained. 4. An arbitrary position other than a measurement point at which the distortion should be measured and a measurement point serving as a reference for the distortion measurement, is obtained in the fourth step at two positions adjacent to each other in the first direction. The weights given to the measurement values are w _x1 and w _x2 , respectively, and the weights given to the measurement values obtained in the fifth step at the two positions adjacent to each other in the second direction are w _y1 and w _y2 , respectively. The distortion measurement method according to claim 1, wherein the relationship of −w _x1 + w _x2 + w _y1 −w _y2 = 0 is satisfied.