JPH1022190A - Method for correcting alignment error in aligner and aligner using it - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a correction parameter deciding method which can be effectively used for correcting the position, etc., of a substrate in an aligner. SOLUTION: The data on the coordinate positions of a plurality of measured alignment marks provided on a substrate on a prescribed coordinate system are obtained by measuring the positions of the alignment marks and corrected coordinate position data are found by converting the obtained coordinate position data by using a function containing at least one correction parameter for correcting data. Then, the correction parameter is decided so that the maximum values of the deviations between the corrected coordinate position data and designed coordinate positions can become the minimum.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for exposing a photosensitive substrate by projecting an image of a pattern formed on a photomask or a reticle onto a photosensitive substrate (wafer) via a projection optical system or directly. The present invention relates to a semiconductor or liquid crystal manufacturing exposure apparatus for transferring a pattern, and particularly to a data correction method suitable for use in position correction of an alignment mark for aligning a photosensitive substrate to a predetermined exposure position in the above-described exposure apparatus. Related to.

[0002]

2. Description of the Related Art When a semiconductor element, a liquid crystal display element, a thin film magnetic head, or the like is manufactured by a photolithography process, a pattern image of a photomask or a reticle (hereinafter, collectively referred to as a "reticle") is exposed through a projection optical system. 2. Description of the Related Art A projection exposure apparatus that projects onto a plurality of shot areas on a wafer to which a material is applied is used. In recent years, as a projection exposure apparatus of this type, a wafer is mounted on a two-dimensionally movable stage, and the wafer is moved (stepped) by this stage.
There is also a so-called step-and-repeat type exposure apparatus that repeats an operation of sequentially exposing a pattern image of a reticle onto each shot area on a wafer, particularly, a reduction projection type exposure apparatus (stepper).

[0003] For example, since a semiconductor element is formed by laminating a large number of circuit patterns on a wafer, when projecting and exposing the circuit patterns of the second and subsequent layers on the wafer, the circuits already exposed on the wafer are exposed. It is necessary to precisely align the pattern with the pattern image of the reticle to be exposed, that is, the alignment (alignment) between the wafer and the reticle. As a conventional method of aligning a wafer in a stepper or the like, the following enhancement method is used.
Global Alignment (hereinafter referred to as "EGA")
(See, for example, JP-A-61-44429).
Reference).

In the EGA system, a plurality of shot areas (chip patterns) each including alignment marks called wafer marks are formed on a wafer, and these shot areas are set in advance on the wafer. Are arranged regularly based on the arranged coordinates. However, even if the wafer is stepped based on the designed arrangement coordinate values (shot arrangement) of a plurality of shot areas on the wafer, for example, the remaining rotation error of the wafer, the orthogonality error of the stage coordinate system (or shot arrangement), Due to factors such as linear expansion and contraction (scaling) of the wafer and offset (parallel movement) of the wafer (center position), the wafer is not always accurately aligned.

The coordinate transformation of the wafer based on these error amounts can be described by a linear transformation equation including six parameters.
Therefore, for a wafer in which a plurality of shot areas including a wafer mark are regularly arranged, the coordinate value of the coordinate system (x, y) on the wafer as the sample coordinate system is changed to the coordinate on the stage as the stationary coordinate system. The primary conversion model for converting to the coordinate values of the system (X, Y) can be expressed as follows using the six conversion parameters a to f.

[0006]

(Equation 1)

[0007] The six conversion parameters a to f in this conversion equation can be determined by, for example, the least squares approximation method. In this case, some of the shot areas (hereinafter, referred to as “sample shots”) selected from a plurality of shot areas (chip patterns) on the wafer are designed on a coordinate system (x, y) associated with each of the shot areas. Coordinates of (x
1, y1), (x2, y2), ..., (xn, y
The position (alignment) of the wafer mark (n) to a predetermined reference position is performed. Then, the coordinate value (xM1, y) in the coordinate system (X, Y) on the stage at that time.
M1), (xM2, yM2),..., (XMn, y
Mn) is actually measured.

In addition, the calculated array coordinates (xi, yi) (i = 1,..., N) of the selected wafer mark are substituted into the above-mentioned first-order conversion model. The difference (Δx, Δy) between the array coordinates (Xi, Yi) and the coordinates (xMi, yMi) measured at the time of alignment is considered as an alignment error. The one alignment error Δx is represented by, for example, the sum of (Xi−xMi) ² with respect to i, and the other alignment error Δy is represented by, for example, the sum of (Yi−yMi) ² with respect to i.

Then, the alignment errors .DELTA.x and .DELTA.y are sequentially partially differentiated by six conversion parameters a to f, an equation is set such that the value becomes zero, and the simultaneous equations are solved by six equations. The conversion parameters a to f are obtained. Thereafter, the alignment of each shot area of the wafer can be performed based on the array coordinates calculated using the primary conversion formulas using the conversion parameters a to f as coefficients.
Alternatively, when the approximation accuracy is not good in the linear conversion formula, the wafer may be aligned using, for example, a quadratic or higher-order formula.

[0010]

As described above, as described above,
In the case of position correction at the time of overlay exposure in the exposure apparatus, positions of a plurality of measurement points on the wafer (alignment mark positions already formed on the wafer in the previous exposure)
Is measured, and the shift (lateral shift), magnification, rotation, and shot area on the wafer are set so as to reduce the deviation between the measured value and an ideal value (an appropriate position at the time of exposure to be performed next specified by the reticle). Correction is performed using a linear (or nonlinear in some cases) function using the orthogonality of the array as a parameter. When correcting a plurality of one-dimensional or multi-dimensional data (or measured values) and its ideal value by a linear or non-linear function including one or more parameters as in this example, the corrected data In the problem of finding a parameter that reduces the deviation from the ideal value, the least squares method is often used. In particular, the least square method has been used as a main means also in position correction at the time of overlay exposure in an exposure apparatus.

However, the least squares method is a method for finding an optimal solution for minimizing the standard deviation of the deviation (error) between the corrected data and the ideal value. Therefore, when the parameters are obtained by using the least squares method, the deviation may be small on average, but a large deviation may remain in one or a small number of data. Because the least squares method is a method that minimizes the standard deviation, even if there is a small number of data with a large deviation, if the deviation of the majority of other data is small, the large deviation is absorbed by those small deviations It is because.

However, for example, in superposition in an exposure apparatus for manufacturing a liquid crystal for a semiconductor or a display device, etc.
If there is at least one point having a large deviation, the product itself becomes defective. In other words, in semiconductor devices and liquid crystal devices, the maximum value of the deviation is more dominant in the product performance than the average magnitude of the deviation as a whole.
As in this example, minimizing the average deviation (in this case, the standard deviation) like the least square method may not always be an industrially optimum solution.

[0013]

SUMMARY OF THE INVENTION The present invention provides a method for performing a correction for minimizing the maximum value of the absolute values of all deviations when performing a data correction calculation, and applies this method to an exposure apparatus and a measuring instrument. Is what you do. As described above, it is possible with some crawling methods to find a correction function that minimizes the maximum value of the deviation of a plurality of data. However, in the crawling method, it is necessary to change the calculation method depending on the number of data and parameters and the assumed mapping formula, which complicates the problem. In addition, since convergence takes time, it is particularly useful for alignment of a substrate which affects the throughput of the apparatus. The problem is that it is inappropriate for use, and it is difficult to find the direction in which the data is optimized in a multidimensional problem with a large number of parameters, and there is a problem that it may converge far from the optimal solution. Not the right way. In addition, there is a problem that automatic calculation is difficult because it is not analytical.

Therefore, the present invention uses the following method. That is, a plurality of one-dimensional or multi-dimensional data is obtained by measurement / measurement, and the data is corrected to an ideal value of the data by a linear or non-linear function including one or more parameters. In the problem of finding a parameter that reduces the deviation between the data and the ideal value, after obtaining the parameter using the weighted least squares method, the weight of the data that maximizes the deviation obtained by that parameter is increased, and the weighting is performed again. By repeating the least squares method, the maximum value of the absolute value of the deviation between all the correction data and the ideal value is minimized by automatic calculation.

Alternatively, the same method can be used for a problem of approximating (fitting) a plurality of one-dimensional or multidimensional data with a linear or non-linear function using one or more parameters.

An example of approximation will be described using a specific equation.
Now, assuming that there are N pairs of data (Xi, yi), f (x)
= Ax + b is assumed to be approximated by a linear expression.

In the weighted least squares method, a function called an evaluation function is represented by

(Equation 2) And then

(Equation 3) A, b that satisfies

(Equation 4) Will be required. Here w _i is a weighting according to each point. It should be noted that the ordinary least squares method, all of w _i may be considered a special case to be a 1.

Now, the method of the present invention performs the following continuation processing without terminating the calculation processing. First using the parameters a, b obtained above, the deviation of each data (approximation _{error), △ y i = | f} (x i) -y i | seek, of searching for the largest ones. Next, add the weight applied to the points with a maximum of deviation as of _{W i ← W i + △ W} i. [Delta] w _i may be a constant for each point.

Thereafter, the weighted least squares method is repeated. As described above, the maximum deviation gradually decreases by repeating the weighted least squares method of sequentially increasing the weight of the point having the maximum deviation.

FIG. 1 shows the relationship between the number of calculations and the maximum deviation.
As the calculation is repeated, the reduction of the maximum deviation becomes slow. Here, the convergence of the calculation is determined, and the repetition is stopped. There are two possible convergence states, and based on this, it is determined that the calculation should be repeatedly stopped. One is when the maximum deviation does not change significantly for a specified number of consecutive times (FIG. 1 (a)), and the other is when the maximum deviation is larger than the smallest maximum deviation value for all consecutive times (FIG. 1 (b)). It is.

It is preferable to determine whether the maximum deviation is larger or smaller than the smallest maximum deviation value by setting a predetermined amount of allowable error band. That is, once the smallest maximum deviation value Δy _min can be obtained, an allowable error band of [Δy _min −ε, Δy _min + ε] is set (ε is an allowable error). Thereafter, each time the maximum deviation is calculated, the result is determined to be of three types, such as larger if it is above the allowable band, small if it is below, and equal if it is within the allowable band.

If the state is "equivalent" continuously for a predetermined number of times or "equal" or "large" continuously for a predetermined number of times, it is determined that further significant improvement of the numerical value cannot be expected. To terminate the calculation. Then, the weight that obtains the smallest maximum deviation in each generation is adopted as the final result. The method of the present invention described above is shown as a flowchart in FIG.

[0023]

According to the present invention, it is possible to improve the performance of a semiconductor manufacturing equipment product whose characteristics are defined not by standard deviation but by a maximum value, a minimum value, and a maximum value-minimum value. In particular, it can be used for calculating and calculating parameters performed at the time of alignment at the time of superposition in a semiconductor or liquid crystal exposure apparatus.

This calculation is performed by measuring a plurality of alignment marks already formed on the target device at the time of overlay exposure, and then using this measurement result to obtain a coordinate correction parameter of a pattern to be overlay exposed. is there. These parameters are x and y shifts,
There are magnifications in both the x and y directions, rotation of the pattern arrangement, orthogonality of the arrangement, and the like. The effect of each parameter on the two-dimensional coordinates x, y is

(Equation 5) Can be represented by Where ξ and η are x, y shifts, γ
_x, the gamma _y x, the rotation of the y magnification, theta pattern sequence, phi is the orthogonality of the array. Further, x and y are measured deviations of each mark from ideal values, X and Y are set coordinate positions of the marks, and x 'and y' are residual coordinate deviations after applying a parameter. x, y, X and Y exist as many as the number of marks.

If the parameters obtained by the present invention can be obtained for all x and y, the maximum values of | x '| and | y' | can be reduced as compared with the conventional methods. In this case, the evaluation function is S = Σ (Wx ′ ² + Vy ′ ² ). w and v are weights applied to the x and y coordinates, respectively. Depending on the process, the quality of one of the x and y axes may be more important. In such a case, the weight of the important axis may be set higher. If the importance of x; y is equal, the calculation proceeds with w = v.

In the manufacture of semiconductors and liquid crystal devices, it is a matter of course that an error at the time of superposition is an important performance factor. If there is an error, there are device types whose overall performance is poor. This type of device has the drawback that the conventional method using the least squares method has a high defect rate and low product performance. In contrast, using this method can reduce such disadvantages.
It can be expected to improve the non-defective rate and product performance.

The actual difference between the correction by the correction method and the correction by the conventional method will be described. First, as a simple example, a case where only shifts in the x and y directions are corrected will be described.
Now, it is assumed that the pattern on the device is formed by a lattice having a partly distorted portion drawn by a dotted line as shown on the left side of FIG. At the time of alignment, the positions of some of these lattice points are measured. When parameters are obtained from the measurement results by the conventional least square method and the patterns are superposed and exposed, the result is as shown in FIG. It can be seen that the superposition error is large in places where there is distortion while points other than the pattern distortion at the upper right of the device are well overlapped. On the other hand, when the superimposed coordinates are obtained by the method of the present invention, the result is as shown in FIG. The error in the upper right portion, which was large in FIG. 3B, has been reduced.

In a semiconductor / liquid crystal device, the maximum deviation in the device is often dominant in product performance, and in such a case, the method of the present invention can provide an accurate correction method.

[0029]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An exposure apparatus for manufacturing a semiconductor or a liquid crystal as an embodiment of the present invention will be described below. FIG. 5 is a diagram schematically illustrating the apparatus of the embodiment. The apparatus projects and exposes a pattern on a reticle (photomask) 4 installed in the apparatus onto a photosensitive substrate (wafer) 7 mounted on a stage 8 via a projection optical system 5.

The stage 8 can be moved by the drive unit 10 in the X and Y directions perpendicular to each other in the plane perpendicular to the optical axis of the projection optical system of the substrate 7 under the control of the control unit 11. The movement amount or position of the stage is constantly measured at a resolution of, for example, about 0.01 μm by interferometers 9 (only one is shown) provided in the X direction and the Y direction. The interferometer 9 is fixed to the apparatus main body and forms a stage coordinate system which is an absolute coordinate system in the apparatus.

As an example, the reticle 4 shown in FIG.
One reticle alignment mark 4a, 4b is formed. The exposure apparatus is a reticle alignment optical system 1a, 1b
These are used to observe the reticle alignment marks 4a and 4b, respectively, and align the reticle at a predetermined position. The reticle alignment optical systems 1a and 1b have alignment sensors 2a and 2b and objective lenses 3a and 3b, respectively. Reticle alignment optical system 1a,
1b is fixed at a predetermined position with respect to the apparatus main body (in other words, with respect to the optical axis of the projection optical system).
By setting the reticle 4 so that the reticle alignment marks 4a and 4b of the reticle coincide with the observation points of the reticle alignment optical systems 1a and 1b, respectively, the reticle is positioned at a predetermined position. There are various configurations of the reticle alignment optical system and various methods of positioning using the reticle alignment optical system. Since each of them is publicly known, a detailed description thereof will be omitted, and only a brief description will be given above.

The exposure apparatus includes a substrate alignment optical system 6a,
6b for aligning the substrate mounted on the stage 8. More specifically, the stage 8 is moved so that the observation mark of the substrate alignment optical systems 6a and 6b coincides with the alignment mark already formed together with the semiconductor or liquid crystal circuit pattern on the substrate,
The measured coordinate position of the alignment mark in the stage coordinate system is obtained from the measured value of the interferometer 9 at that time. There are various known methods for the configuration of the substrate alignment optical system as in the case of the reticle alignment optical system, but the description is omitted here.

The obtained measurement coordinate position is stored in a memory provided in the exposure apparatus. Using the measured coordinate position data stored in the memory, a correction parameter according to the method of the present invention is calculated by a digital processor such as a microcomputer also provided in the exposure apparatus, and according to the parameter obtained by the calculation. Then, the stage 8 is moved. For example, for the substrate shift, the obtained X, Y
The stage is shifted in the X and Y directions according to the shift parameter. To correct the magnification, the lens magnification is adjusted by a method such as changing the air pressure inside the lens. Other position corrections are performed according to the respective parameters, and then the overlapped exposure is performed at the corrected positions.

In the following, an example of a simulation to which the correction method of the present invention is applied when four alignment marks capable of measuring positions in the xy2 directions are arranged on a substrate will be described.

The error between the designed coordinate position of each mark and the measured position of the mark relative to it is as shown in Table 1 below.

[Table 1]

Here, the maximum deviation at the measured position before the correction is the error amount 1.2,000 of the X coordinate of the fourth mark.
μm.

Here, the calculation was performed with three correction parameters of x, y shift ξ, η and rotation θ. In this case, the conversion equation for position correction is as follows.

(Equation 6) The evaluation function is S = 関 数 (Wx ′ ² + Vy ′ ² ) as described above.

Table 2 below shows the results including the progress of the calculation. The number of calculations is the number of repeated calculations performed according to the method of the present invention. When this is 0, it represents the original amount of deviation of the mark. When 1, the weight of each position error
Calculation is performed according to the conventional least squares method where w and v are all equal. From the second time onward, the calculation is performed by increasing the weight of the data showing the maximum deviation in the previous calculation. As shown in Table 2, the maximum deviation amount gradually decreased as the number of calculations was further increased using this method.

Finally, the least squares solution is 0.4250
[Μm], whereas the method uses 0.3576 [μm].
m].

[Table 2] According to the method of the present invention as described above, for example, when the displacements of the four alignment marks are as represented by the four vectors in FIG. By moving the substrate to the position drawn by the dotted line in FIG. 4B according to the parameters of the y shift and rotation, the maximum value of the deviation can be reduced as shown in the figure.

It is to be noted that a similar effect can be obtained by considering this as a process correction. That is, it is assumed that the state of superposition of the pattern of the substrate on which the superposition exposure has already been completed has already been measured. Table 1 shows the position of the pattern,
This example can be used for calculating a parameter for improving a process, assuming that the shift amount of a superimposed pattern with respect to a pattern to be superimposed. In other words, after the test exposure is performed once, an appropriate parameter is obtained from the measurement of the overlapping state of the patterns, and a more accurate correction value is obtained by applying the correction value to the actual main exposure.

In the exposure apparatus of the above embodiment, the position measurement is performed using the exposure apparatus itself, but a separate measurement apparatus may be used. In this embodiment, the correction calculation at this time is performed by the processor of the exposure apparatus itself. However, the correction calculation may be performed by the above-described separate measuring apparatus or another computer.

This calculation method can also be applied to alignment on the reticle side. Generally, alignment of a reticle is performed by aligning two or more alignment marks formed on the reticle with an alignment sensor on the apparatus.

For example, in the case of an apparatus having an alignment mark as shown in FIG. 5 and reticle alignment sensors 1a and 1b as shown in FIG. 5, alignment is performed and x ·
Assume that the alignment is completed with an error of y. In this case, if the correction of the xy shift, the magnification, and the rotation (ξ, η, γ, θ) is performed, the error of the xy becomes the following equation x ′ · y ′.

(Equation 7) Appropriate parameters (ξ, η, γ, θ) at this time may be calculated according to this method using S = Σ (Wx ′ ² + Vy ′ ² ) as an evaluation function.

Further, in a liquid crystal device, a screen splicing and a superposition difference of adjacent patterns at a screen splicing portion are important factors, but the method can be applied.

The present method can be applied to the apparatus manufacturing process of the exposure apparatus itself (that is, the adjustment and inspection steps of the apparatus) and the process technology in the semiconductor or liquid crystal manufacturing process.

In the actual device adjustment process, there is a process that should be referred to as fine adjustment of the device. This is an important apparatus performance in which, for example, the overlay accuracy of the exposure apparatus, lens distortion, screen splicing accuracy, etc., must be adjusted so as to satisfy the standard values. For this purpose, mechanical or electrical adjustment is required, but in the final stage, an error peculiar to each device remains. In order to eliminate the residual error, that is, the habit of the apparatus, a method of obtaining and recording an adjustment amount for the apparatus is used.

That is, for example, when it is assumed that a certain error of ξ · η · γ _x · γ _y · θ · φ occurs when an overlay inspection is performed, these amounts are recorded in an apparatus and exposed. It is reasonable to adjust these amounts to determine the exposure coordinates.

The adjustment value may be recorded in a control device (computer or the like) of the apparatus. If the least-squares method of the related art is used in calculating the adjustment value, optimization adjustment that minimizes the standard deviation can be performed.

On the other hand, some of the standards for the device accuracy are specified not by the standard deviation but by the maximum value and the minimum value. In such a standard, the solution of the least square method may not always be the optimum solution. Absent. By using this method, it is possible to obtain an optimal solution even in such a case, it is possible to rationalize the accuracy of the device in the device manufacturing process, and in the process of manufacturing a semiconductor using the device. Each has the advantage that a more tightly tuned device can be used.

In the semiconductor manufacturing process, the present method can be further used to improve the production process. In the production process, there is a residual error which is not a factor of the exposure apparatus similar to the residual error of the above-described apparatus. For example, in steps other than the exposure step, there is a step of processing the substrate at a high temperature, and the influence of thermal expansion of the substrate may remain. Such an error factor may cause a problem in accuracy such as the above-described overlay accuracy in the exposure process.

In this case, the process can be properly adjusted in the same manner as the above-described adjustment of the exposure apparatus. That is, while the above-described adjustment is an adjustment of the individual apparatus, the adjustment here is an adjustment of a process, that is, an adjustment of an exposure apparatus for each production process of a semiconductor or the like.

As in the above-described method, if these adjustment values are calculated and recorded in the apparatus as adjustment values for each process, the process can be improved. Also in this case, if the present method is applied, the suitability of the process can be increased, which is beneficial for improving the performance of semiconductors and the like and improving the yield rate.

Regarding the apparatus adjustment method or the process adjustment method described above, in addition to the adjustment of x shift, y shift, x magnification, y magnification, substrate rotation, array orthogonality in the case of the substrate alignment, the x shift of the mask, The present invention is also applicable to adjustment of y shift, magnification, and mask rotation.

In the apparatus adjustment process, not only the alignment-related adjustment process but also mechanical and electrical adjustment can be applied. For example, the distortion standard of the projection lens of the device is generally specified as "maximum", and adjustments are made to conform to this standard.

Distortion adjustment is performed by making use of the fact that if the distance / inclination between the plurality of optical lenses in the projection lens is finely adjusted, the characteristic of distortion changes.
The distance and inclination between lenses to be fine-tuned can be obtained based on the current distortion data and the relationship between the amount of change in distortion and the change in distance and inclination between optical lenses. At present, calculation by the least squares method is common. Also in this case, if the present method is used, a more appropriate fine adjustment amount can be obtained, and as a result, adjustment can be rationalized.

In addition, the method of the present invention can be widely used as long as the problem is to calculate a more appropriate parameter from a plurality of data.

[0057]

In the semiconductor / liquid crystal device, the maximum deviation in the device is often dominant in the product performance, and in such a case, the method of the present invention can provide an accurate correction method. That is, the performance of the product can be improved in order to provide a more accurate correction method than the ordinary least square method. It also contributes to improving yield.

[Brief description of the drawings]

FIGS. 1A and 1B are graphs showing examples of convergence of optimization by the present method.

FIG. 2 is a flowchart of a calculation method according to the present invention.

FIG. 3 is a diagram showing an example of a difference between a result obtained by the present method and a result obtained by a conventional method.

FIG. 4 is an explanatory diagram showing an example of position shift correction for superposition.

FIG. 5 is a diagram schematically showing a configuration of an exposure apparatus according to an embodiment of the present invention.

6 is a diagram showing an example of a reticle used in the apparatus of the embodiment in FIG.

[Explanation of symbols]

 1a, 1b: reticle alignment optical system 2a, 2b: alignment sensor 3a, 3b: objective lens 4: reticle 5: projection optical system 6a, 6b: substrate alignment optical system 7: substrate 8: stage 9: interferometer 10: drive unit 11: Control unit

Claims (12)

[Claims] 1. A method for measuring the positions of a plurality of marks on a substrate to obtain data of the measured coordinate positions of the plurality of alignment marks in a predetermined coordinate system, and correcting the obtained plurality of data for the data. The corrected position coordinate data is obtained by performing conversion using a function including at least one correction parameter, and a maximum deviation among deviations between the plurality of corrected coordinate position data and the respective designed coordinate positions is determined. A method of correcting a substrate alignment error, wherein the correction parameter is determined so as to be substantially minimum. 2. When determining the correction parameter, a correction parameter is obtained by a weighted least squares method.
The weight of the data in which the deviation between the corrected coordinate position data calculated by the obtained correction parameter and the designed coordinate position is maximized is increased, and the weighted least squares method is repeated to asymptotically increase the maximum. 2. The method according to claim 1, wherein the deviation is substantially minimized. 3. The method according to claim 2, wherein a predetermined allowable range of the minimum value of the maximum deviation is set, and the maximum deviation between the correction data obtained by performing the weighted least squares method and the designed coordinate position. Each time is obtained, the maximum deviation at that time is compared with the maximum deviation of the historical minimum, and the maximum deviation at that time falls within the predetermined allowable range with respect to the maximum deviation of the historical minimum, or the maximum deviation at that time is A method of correcting a positioning error of a substrate, comprising determining that a maximum deviation has substantially reached a minimum when a larger number of consecutive deviations than a maximum deviation of the successive generations has become larger than a predetermined number of times, and determining a correction parameter. 4. The method according to claim 1, wherein the correction method is applied at the time of overlay exposure in an exposure apparatus for manufacturing a semiconductor or a liquid crystal for exposing and transferring a pattern formed on a mask onto a photosensitive substrate. 4. The method according to claim 1, wherein the alignment mark is an alignment mark accompanying a pattern already exposed on the substrate. 5. The method according to claim 1, wherein the correction parameter is related to at least one of a lateral shift of the substrate position, a rotation, a magnification when projecting the pattern on the mask onto the substrate, and an orthogonality of the pattern arrangement on the substrate. 5. The method according to claim 4, wherein the positioning error is corrected. 6. An exposure apparatus for manufacturing a semiconductor or a liquid crystal display device for transferring a pattern formed on a mask by exposing a photosensitive substrate through the mask, wherein the exposure apparatus has already been exposed on the substrate. A coordinate position detecting means for detecting coordinate positions of a plurality of alignment marks associated with the pattern in a predetermined coordinate system in the apparatus and obtaining coordinate position data; and a method for correcting the plurality of obtained data by correcting the data. Means for correcting the coordinate position data by converting the coordinate position data by a function including one or more correction parameters, wherein a maximum deviation among deviations between the corrected plurality of coordinate position data and respective designed coordinate positions. Coordinate position data correcting means for determining the correction parameter so that the deviation of the correction parameter is substantially minimized, and using the determined correction parameter, An exposure apparatus comprising: substrate position control means for correcting a substrate position when a pattern formed on a mask is overlaid on a pattern already formed on a substrate for exposure. 7. The coordinate position data correcting means obtains a correction parameter by a weighted least squares method when determining the correction parameter, and calculates the corrected coordinate position data calculated based on the obtained correction parameter and the designed coordinate position. 7. The exposure apparatus according to claim 6, wherein the maximum deviation is substantially asymptotically reduced by increasing the weight of the data having the maximum deviation and repeating the weighted least squares method again. . 8. The coordinate position data correction means sets a predetermined allowable width of a minimum value of a maximum deviation when determining the correction parameter, and calculates the correction data obtained by performing the weighted least squares method and the design data. Each time the maximum deviation of the coordinate position is obtained, the maximum deviation at that time is compared with the maximum deviation of the past, and the maximum deviation at that time falls within the predetermined allowable range for the maximum deviation of the past, or The method according to claim 7, wherein when the maximum deviation at that time becomes larger than the minimum deviation of the successive generations for a predetermined number of times, it is determined that the maximum deviation has substantially reached the minimum, and the correction parameter is determined. Exposure equipment. 9. The method according to claim 1, wherein the correction parameter is related to at least one of a lateral shift of the substrate position, a rotation, a magnification at the time of projecting the pattern on the mask onto the substrate, and an orthogonality of the pattern arrangement on the substrate. The exposure apparatus according to claim 6, wherein 10. A method for adjusting a plurality of amounts related to the operation accuracy of an exposure apparatus, wherein the measurement data of the plurality of amounts is acquired, and the acquired data is obtained by a function including an adjustment parameter for adjusting the plurality of amounts. A plurality of correction data is obtained by converting a plurality of data, and the adjustment parameter is set so that a maximum deviation among deviations of each of the correction data and respective ideal values of the plurality of amounts is substantially minimum. A method for adjusting an exposure apparatus, comprising: determining an adjustment based on the determined adjustment parameter. 11. When determining the parameter,
Obtain a parameter by a weighted least squares method, increase the weight of the data in which the deviation between the plurality of correction data calculated by the obtained parameter and its ideal value is the largest, and perform the weighted least squares method again. 11. The method according to claim 10, wherein the maximum deviation is asymptotically minimized by repeating the process. 12. A digital processor calculates correction data obtained by converting a plurality of one-dimensional or multidimensional data obtained by measurement and stored in a memory by a linear or non-linear conversion function including one or more parameters. By this, in the method of obtaining a parameter that minimizes the maximum of the deviation between the plurality of correction data and the ideal value of each data, in obtaining the correction data, using a weighted least squares method By calculating the parameters, calculating the deviation from the respective ideal values of the correction data obtained by the parameters, increasing the weight of the data with the maximum deviation, and repeating the weighted least squares method again, Determine the parameters so that the maximum value of the deviation between the correction data and each ideal value is substantially minimized A data correction method.