JPH06291021A - Alignment method - Google Patents

Abstract

PURPOSE:To perform highly accurate alignment on the entire surface of a substrate by performing the alignment by excluding measured results in the case where the results contain measurement errors and, in the case of in a locally distorted area, mainly based on the measured results of a sample area in the area. CONSTITUTION:When the nonlinear error of a specific area SA7 has the same trend as the nonlinear errors of areas to be processed SA71-SA78 around the area SA7, the alignment of the local area SA7 is performed based only of the measured results of its periphery by considering that the nonlinear error of the area SA7 is caused by the local nonlinear strain of a substrate W. When the nonlinear error of the area SA7 has a different trend, on the other hand, the alignment is performed by excluding the measured results of the area SA7 by considering that the results are erroneous. The exposure of the area SA7 is performed after the alignment is performed by using a die-by-die system or based on the measured results of a sample area other than the specific area.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a projection exposure apparatus which sequentially exposes a pattern image of a reticle on each shot area of a wafer on the basis of array coordinates calculated by statistical processing. The present invention relates to a position alignment method suitable for application in alignment.

[0002]

2. Description of the Related Art When a semiconductor device, a liquid crystal display device, or the like is manufactured by a photolithography process, a photosensitive material is applied with a pattern image of a photomask or reticle (hereinafter referred to as "reticle") through a projection optical system. A projection exposure apparatus is used to project each shot area on a wafer.
In recent years, as a projection exposure apparatus of this type, a wafer is placed on a stage that is two-dimensionally movable, and the wafer is stepped by this stage to form a pattern image of a reticle on each shot area on the wafer. A so-called step-and-repeat type exposure apparatus that repeats the operation of sequentially performing exposure, especially a reduction projection type exposure apparatus (stepper) is often used.

For example, since a semiconductor element is formed by stacking multiple layers of circuit patterns on a wafer, when projecting and exposing the circuit patterns of the second and subsequent layers, the circuit patterns are already formed on the wafer. Further, it is necessary to accurately align each shot area with the pattern image of the reticle, that is, accurately align the wafer and the reticle. A conventional wafer alignment method in a stepper or the like is roughly as follows (for example, Japanese Patent Laid-Open No. 61-61).
44429).

That is, a plurality of shot areas (chip patterns) each including a positioning mark called a wafer mark are formed on the wafer, and these shot areas are arranged in advance on the wafer. Are regularly arranged based on. However, even if the wafer is stepped based on the designed array coordinate values (shot arrays) of a plurality of shot areas on the wafer, the wafer is not always accurately aligned due to the following factors.

(1) Remaining rotation error of wafer θ (2) Orthogonal error of stage coordinate system (or shot arrangement) w (3) Linear expansion and contraction (scaling) of wafer Rx, Ry (4) Wafer (center position) Offset (translation) O
x, Oy

At this time, the coordinate transformation of the wafer based on these four error amounts (six parameters) can be described by a linear transformation equation. Therefore, for a wafer in which a plurality of shot areas including wafer marks are regularly arranged, the coordinate system (x, y) on the wafer is converted to the coordinate system (X, Y) on the stage as a stationary coordinate system. The first-order conversion model can be expressed as follows using the six conversion parameters a to f.

[0007]

[Equation 1]

The six conversion parameters a to f in this conversion formula are the enhanced global alignment (hereinafter referred to as “EG” using the least square approximation method as follows.
A)) method. In this case, each of several exposure shots (hereinafter referred to as “sample shots”) selected from a plurality of shot areas (chip patterns) to be exposed on the wafer (hereinafter referred to as “exposure shots”) The associated coordinate system (x,
The design coordinates on (y) are (x1, y1) and (x
2, y2), ..., (Xn, yn) are aligned with a predetermined reference position. Then, the actual coordinate values (XM1, YM1) and (XM) in the coordinate system (X, Y) on the stage at that time
M2, YM2), ..., (XMn, YMn) are measured.

Further, the calculated array coordinates (xi, yi) (i = 1, ..., N) of the selected wafer marks are substituted into the above-mentioned linear transformation model to obtain the calculated array coordinates. (Xi, Yi) and the measured coordinates (X
The difference (Δx, Δy) from Mi, YMi) 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 with the six conversion parameters a to f, an equation is set so that the value becomes 0, and these six simultaneous equations are solved. For example, six conversion parameters a to f are obtained. After that, the alignment of each shot area of the wafer can be performed based on the array coordinates calculated by using the linear conversion equation having the conversion parameters a to f as coefficients.
Alternatively, when the approximation accuracy is not good in the primary conversion formula, the wafer may be aligned by using, for example, a second or higher order formula.

[0011]

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention
In the alignment method of the A method, a plurality of sample shots may include a so-called jump shot in which the nonlinear error amount obtained by subtracting the linear error amount from the alignment error is particularly large as compared with other sample shots. there were. It is desirable to change the countermeasure depending on whether such a jump shot is due to a measurement error due to a collapse of a wafer mark belonging to the sample shot on the wafer or due to local non-linear distortion on the wafer. . That is, if the jump shot is due to a measurement error, the measurement result must be excluded,
If the jump shot is due to local distortion, it is desirable to perform alignment by distinguishing the locally distorted area from other areas.

However, conventionally, it was considered that the jump shots were uniformly caused by measurement errors, and the measurement results were not used. This is because there was no highly accurate alignment method that could cope with local distortion. Therefore, the conventional alignment method has a disadvantage that the overlay accuracy in the periphery of the jump shot is lower than the overlay accuracy in other areas.

In view of the above point, the present invention obtains a conversion parameter by statistical processing based on the result obtained by actually measuring the position of the sample shot on the wafer to be processed in advance, and calculates this conversion parameter. In the alignment method for aligning each exposure shot on the wafer based on the calculated array coordinates calculated by using, even if there is a jump shot having a particularly large non-linear error amount in the sample shot, the entire surface of the wafer The purpose is to be able to align with high accuracy.

[0014]

The alignment method according to the present invention is carried out on a sample coordinate system (x, y) set on a substrate (W) as shown in FIGS. 1 and 5 to 9, for example. Each of the plurality of processed regions (ESi) arranged on the substrate (W) based on the arrangement coordinates has a predetermined processing position within a stationary coordinate system (X, Y) that defines the movement position of the substrate (W). Multiple regions to be machined (ESi)
Of the substrate by measuring the coordinate positions of at least three preselected sample areas (SA1 to SA8) on the static coordinate system (X, Y), and statistically calculating the plurality of measured coordinate positions. The array coordinates of each of the plurality of processed regions (ESi) on (W) on the static coordinate system (X, Y) are calculated, and according to the calculated array coordinates of each of the plurality of processed regions (ESi). The present invention relates to a method of aligning each of a plurality of processed regions (ESi) with respect to the processing position by controlling the moving position of the substrate (W).

Then, the present invention provides a sample area (SA1
To SA8), a first step (step 101) of measuring the coordinate position on each stationary coordinate system (X, Y);
From the coordinate position measured in the first step, each stationary coordinate system (X, Y) of the sample area (SA1 to SA8)
The second step (step 102) of obtaining the non-linear error amount of the coordinate position above, and a plurality of sample areas (SA1 to SA).
8) The processed area (SA71 to SA) around the singular area (SA7) whose non-linear error amount exceeds a predetermined allowable value.
78), the third step (step 104) of measuring the coordinate position on the stationary coordinate system (X, Y), and the coordinate positions measured in the first step and the third step are used to determine the area around the peculiar region. And a fourth step (step 105) of obtaining a non-linear error amount of the processing areas (SA71 to SA78).

Then, the non-linear error amount of the processed areas (SA71 to SA78) around the unique area is the unique area (S
In the case of the same tendency as the nonlinear error amount of A7), the singular area (SA7) and the processed area (SA around the singular area)
71 to SA78, the array coordinates on the stationary coordinate system are set to the coordinate position measured in the unique step (SA7 in the first step and the processed area (SA71 to S71) around the unique area.
The coordinate position measured in the third step of A78) is calculated by statistically calculating (step 107), and the non-linear error amount of the processed areas (SA71 to SA78) around the unique area is the unique area (SA7). In the case of a tendency different from the amount of nonlinear error, the coordinate position measured in the first step and the third step excluding the coordinate position measured in the first step for the singular area (SA7) is statistically calculated, and thus the workpiece is processed. The array coordinates of each area (ESi) on the static coordinate system (X, Y) are calculated (step 110).

[0017]

According to the alignment method of the present invention, a peculiar region having a large non-linear error amount in the sample regions (SA1 to SA8) selected from the processed region (ESi) on the substrate (W). If there is a (flying shot) (SA7), the area to be processed (SA71 to SA78) around it is present.
The coordinate position on the stationary coordinate system (X, Y) is measured and the non-linear error amount is obtained for each. Then, the unique region (S7)
Non-linear error amount and surrounding processed area (SA71 to SA7
If the nonlinear error amount in 8) has the same tendency, the nonlinear error in the singular region (S7) is considered to be caused by the local nonlinear distortion of the substrate (W), and the position of the local region is considered. The matching is performed based only on the measurement result of the surrounding area.

On the other hand, when the non-linear error amount of the singular area (S7) and the non-linear error amount of the peripheral processed areas (SA71 to SA78) tend to be different, the measurement result of the singular area (S7) is a measurement error. Assuming that there is a unique region (S
Positioning is performed by excluding the measurement result of 7). Regarding the unique region (S7), it is possible to perform alignment by a die-by-die method and then perform exposure, or to perform alignment based on the measurement result of the sample region other than the unique region.

[0019]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the alignment method according to the present invention will be described below with reference to the drawings. FIG. 2 shows a schematic configuration of a projection exposure apparatus suitable for applying the alignment method of this embodiment. In FIG.
Illumination light IL generated from the ellipsoidal mirror 2 is reflected by the ellipsoidal mirror 2 and once condensed at its second focus, and then includes illumination optical including a collimator lens, an interference filter, an optical integrator (fly-eye lens), an aperture stop (σ stop), and the like. It is incident on the system 3. Although not shown, the fly-eye lens is arranged in the in-plane direction perpendicular to the optical axis AX so that the reticle-side focal plane of the fly-eye lens substantially coincides with the Fourier transform plane (pupil conjugate plane) of the reticle pattern.

A shutter (for example, a four-blade rotary shutter) 37 for closing and opening the optical path of the illumination light IL by a motor 38 is arranged near the second focal point of the elliptic mirror 2. As the illumination light for exposure, laser light such as an excimer laser (KrF excimer laser, ArF excimer laser) or a harmonic wave of a metal vapor laser or a YAG laser is used in addition to the bright line of the ultra-high pressure mercury lamp 1 or the like. It doesn't matter.

In FIG. 2, illumination light (i-line or the like) IL in a wavelength range for exposing the resist layer emitted from the illumination optical system 3 to light.
Is reflected by the beam splitter 4, and then passes through a first relay lens 5, a variable field stop (reticle blind) 6 and a second relay lens 7, and a mirror 8
Leading to. Then, the illumination light IL reflected by the mirror 8 in a substantially vertically downward direction illuminates the pattern area PA of the reticle R with substantially uniform illuminance via the main condenser lens 9. The arrangement surface of the reticle blind 6 and the pattern formation surface of the reticle R are in a conjugate relationship (image formation relationship), and the drive system 36
Thus, the illumination field of the reticle R can be arbitrarily set by opening and closing the plurality of movable blades that form the reticle blind 6 to change the size and shape of the opening.

In the reticle R of the present embodiment, reticle marks serving as alignment marks are formed at substantially central portions of the four sides of the pattern area PA surrounded by the light-shielding band. By projecting the images of these reticle marks onto the resist layer of the wafer W, the images of these reticle marks are formed as latent images on the resist layer. Further, in this embodiment, those reticle marks are
It is also used as an alignment mark when aligning each reticle R with each shot area of the wafer W. The four reticle marks have the same configuration (however, the directions are different). For example, a certain wafer mark is a diffraction grating mark composed of seven dot marks arranged in the Y direction, and is separated by a predetermined distance in the X direction. It is a multi-mark arranged in 5 columns. The wafer marks are formed by a light-shielding portion such as chrome inside a transparent window provided in the light-shielding band of the reticle R. Further, on the reticle R, alignment marks composed of two cross-shaped light-shielding marks are formed facing each other in the vicinity of the outer periphery of the reticle R. These two alignment marks are used for alignment of the reticle R (positioning with respect to the optical axis AX of the projection optical system 13).

The reticle R is mounted on a reticle stage RS which can be finely moved in the direction of the optical axis AX of the projection optical system 13 by a motor 12, and can be two-dimensionally moved and finely rotated in a horizontal plane perpendicular to the optical axis AX. It is placed. At the end of the reticle stage RS, a movable mirror 11m that reflects a laser beam from a laser light wave interferometer (laser interferometer) 11
Is fixed, and the two-dimensional position of the reticle stage RS is constantly detected by the laser interferometer 11 with a resolution of, for example, about 0.01 μm. Reticle alignment systems (RA systems) 10A and 10B are arranged above the reticle R, and these RA systems 10A and 10B are mounted on the reticle R.
Two cross-shaped alignment marks formed near the outer periphery of the are detected. By finely moving the reticle stage RS based on the measurement signals from the RA systems 10A and 10B, the reticle R is positioned so that the center point of the pattern area PA coincides with the optical axis AX of the projection optical system 13.

The illumination light IL that has passed through the pattern area PA of the reticle R enters the projection optical system 13 that is telecentric on both sides, and is projected by the projection optical system 13 to a projected image of the circuit pattern of the reticle R that is reduced to 1/5. However, a resist layer is formed on the surface, and the surface is projected (imaged) so as to be superposed on one shot area on the wafer W held so that the surface substantially coincides with the best imaging plane of the projection optical system 13. .

The wafer W is vacuum-sucked by a finely rotatable wafer holder (not shown), and is held on the wafer stage WS via this wafer holder. The wafer stage WS is configured to be two-dimensionally movable in a step-and-repeat manner by a motor 16,
When the transfer exposure of the reticle R onto one shot area is completed, the wafer stage WS is stepped to the next shot position. A movable mirror 15 that reflects the laser beam from the laser interferometer 15 is provided at the end of the wafer stage WS.
m is fixed, and the two-dimensional coordinates of the wafer stage WS are constantly detected by the laser interferometer 15 with a resolution of about 0.01 μm, for example. The laser interferometer 15 is
The coordinates of one direction perpendicular to the optical axis AX of the projection optical system 13 of the wafer stage WS (referred to as the X direction) and the Y direction perpendicular thereto are measured, and the coordinates in the X direction and the Y direction are measured. A stage coordinate system (stationary coordinate system) (X, Y) of wafer stage WS is defined. That is, the coordinate value of the wafer stage WS measured by the laser interferometer 15 is the coordinate value on the stage coordinate system (X, Y).

On the wafer stage WS, a reference member (glass substrate) 14 having a reference mark used when measuring a baseline amount (described later) or the like has almost the same height as the exposed surface of the wafer W. Is provided. The reference member 14 has, as a reference mark, a slit pattern composed of five light-transmitting L-shaped patterns and two sets of reference patterns formed of light-reflecting chrome (duty ratio is 1:
1) and are provided. One set of reference patterns is
A diffraction grating mark formed by arranging 7 dot marks arranged in the Y direction in three rows in the X direction, a diffraction grating mark formed by arranging three linear patterns in the X direction, and 12 extending in the Y direction. The bar marks of the book are arranged in the X direction. The other set of reference patterns is the one set of reference patterns rotated by 90 °.

Now, the slit pattern formed on the reference member 14 is illuminated from below (inside the wafer stage) by the illumination light (exposure light) transmitted below the reference member 14 using an optical fiber (not shown) or the like. Is configured to. The illumination light transmitted through the slit pattern of the reference member 14 forms a projected image of the slit pattern on the back surface (pattern surface) of the reticle R via the projection optical system 13. Further, the illumination light passing through any of the four reticle marks on the reticle R reaches the beam splitter 4 through the main condenser lens 9, the relay lenses 7 and 5, and the like.
The illumination light transmitted through the beam splitter 4 is received by a photoelectric detector 35 arranged near the pupil conjugate plane of the projection optical system 13. The photoelectric detector 35 outputs a photoelectric signal SS corresponding to the intensity of the illumination light to the main control system 18. In the following, an optical fiber (not shown), the reference member 14 and the photoelectric detector 3
5 is collectively called an ISS (Imaging Slit Sensor) system.

Further, in FIG. 2, an image formation characteristic correction unit 19 capable of adjusting the image formation characteristic of the projection optical system 13 is also provided.
The imaging characteristic correction unit 19 in this embodiment is the projection optical system 1
Some of the lens elements that make up part 3, especially reticle R
By independently driving (moving or tilting in a direction parallel to the optical axis AX) each of the plurality of lens elements close to each other by using a piezoelectric element such as a piezo element, For example, it corrects projection magnification and distortion.

Next, an off-axis type alignment sensor (hereinafter referred to as "Field Imag") is provided on the side of the projection optical system 13.
e Alignment system (FIA system) ”is provided. In this FIA system, the light generated by the halogen lamp 20 is converted into the condenser lens 21 and the optical fiber 22.
It is guided to the interference filter 23 through the light source, and the light in the photosensitive wavelength region and the infrared wavelength region of the resist layer is cut off there. The light transmitted through the interference filter 23 enters the telecentric objective lens 27 via the lens system 24, the beam splitter 25, the mirror 26 and the field stop BR. The light emitted from the objective lens 27 is reflected by a prism (or mirror) 28 fixed around the lower part of the lens barrel of the projection optical system 13 so as not to block the illumination visual field of the projection optical system 13, and the wafer W is almost vertical. To irradiate.

The light from the objective lens 27 is applied to the partial area including the wafer mark (base mark) on the wafer W, and the light reflected from the area is the prism 28, the objective lens 27, the field stop BR, and the mirror 26. , Is guided to the index plate 30 via the beam splitter 25 and the lens system 29. Here, the index plate 30 is arranged in a plane conjugate with the wafer W with respect to the objective lens 27 and the lens system 29, and the image of the wafer mark on the wafer W is formed in the transparent window of the index plate 30. Further, the index plate 30 is formed with two linear marks extending in the Y direction at predetermined intervals in the X direction as index marks in the transparent window.
The light that has passed through the index plate 30 receives the first relay lens system 31,
The image of the wafer mark and the image of the index mark are formed on the light receiving surface of the image pickup device 34 by being guided to the image pickup device (CCD camera etc.) 34 via the mirror 32 and the second relay lens system 33. The image pickup signal SV from the image pickup device 34 is supplied to the main control system 1
8, the position (coordinate value) of the wafer mark in the X direction is calculated. Although not shown in FIG. 2, in addition to the FIA system having the above configuration (FIA system for X axis),
Another set of FIA for detecting mark position in Y direction
A system (FIA system for Y axis) is also provided.

Next, TT is provided on the upper side of the projection optical system 13.
An L (through the lens) type alignment sensor 17 is also arranged, and the position detection light from the alignment sensor 17 is transmitted through the mirrors M1 and M2 to the projection optical system 1.
It is led to 3. The light for detecting the position is the projection optical system 1
The wafer W on the wafer W is irradiated with the reflected light from the wafer W via the projection optical system 13, the mirror M2, and the mirror M1, and the alignment sensor 17
Returned to. The alignment sensor 17 obtains the position of the wafer mark on the wafer W from the signal obtained by photoelectrically converting the returned reflected light.

FIG. 3 shows a detailed structure of the TTL type alignment sensor 17 in FIG. 2. In FIG. 3, the alignment sensor 17 of this example is a two-beam interference type alignment system (hereinafter referred to as “LIA system”). ) And a laser step alignment type alignment system (hereinafter referred to as “LSA system”), and the optical members thereof are maximally shared. Although briefly described here, a more specific configuration is disclosed in Japanese Patent Laid-Open No. 2-272305.

In FIG. 3, a laser beam emitted from a light source (He-Ne laser light source, etc.) 40 is split by a beam splitter 41, and the laser beam reflected here is passed through a shutter 42 to a first beam shaping optical system. (LI
A optical system) 45. On the other hand, the laser beam transmitted through the beam splitter 41 enters the second beam shaping optical system (LSA optical system) 46 via the shutter 43 and the mirror 44. Therefore, the shutters 42 and 43
Can be used by switching between the LIA system and the LSA system by appropriately driving.

The LIA optical system 45 includes two sets of acousto-optic modulators and the like, and emits two laser beams having a predetermined frequency difference Δf substantially symmetrically with respect to the optical axis.
Further, the two laser beams emitted from the LIA optical system 45 reach the beam splitter 49 via the mirror 47 and the beam splitter 48, and the two laser beams transmitted therethrough are a lens system (inverse Fourier transform lens). 5
The light enters the reference diffraction grating 55, which is fixed on the apparatus, from two different directions at a predetermined crossing angle, and forms an image (crossing) through the mirror 3 and the mirror 54. The photoelectric detector 56 receives the interference light of the diffracted lights that are transmitted through the reference diffraction grating 55 and generated in substantially the same direction, and outputs a sinusoidal photoelectric signal SR corresponding to the intensity of the diffracted light to the main control system 18 (FIG. 2))
It is output to the A arithmetic unit 58.

On the other hand, the two laser beams reflected by the beam splitter 49 intersect once at the opening of the field stop 51 by the objective lens 50, and then the mirror M2 (see FIG. 2).
The inside mirror M1 is incident on the projection optical system 13 via a mirror (not shown). Further, the two laser beams incident on the projection optical system 13 become substantially symmetrical with respect to the optical axis AX on the pupil plane of the projection optical system 13 and once converged in a spot shape. The parallel luminous fluxes are inclined with respect to the direction (Y direction) with respect to each other with the optical axis AX in between, and become parallel luminous fluxes, which are incident on the wafer mark from two different directions at a predetermined crossing angle. A one-dimensional interference fringe that moves at a speed corresponding to the frequency difference Δf is formed on the wafer mark, and the ± first-order diffracted light (interference light) generated in the same direction from the mark, that is, the optical axis direction in this case, is projected by the projection optical system. The light is received by the photoelectric detector 52 via the system 13, the objective lens 50, etc., and the photoelectric detector 52 receives the sine-wave photoelectric signal S corresponding to the cycle of the change in brightness of the interference fringes.
Dw is output to the LIA operation unit 58. The LIA calculation unit 58 calculates the position deviation amount of the wafer mark from the phase difference on the waveforms of the two photoelectric signals SR and SDw, and uses the position signal PDs from the laser interferometer 15 to calculate the position deviation amount. The coordinate position of the wafer stage WS when it becomes zero is obtained, and this information is output to the alignment data storage unit 61 (see FIG. 4).

The LSA optical system 46 includes a beam expander, a cylindrical lens, etc., and the laser beam emitted from the LSA optical system 46 enters the objective lens 50 via the beam splitters 48 and 49. Further, the laser beam emitted from the objective lens 50 once converges into a slit shape at the opening of the field stop 51, and then enters the projection optical system 13 via the mirror M2. The laser beam incident on the projection optical system 13 passes through almost the center of its pupil plane, then extends in the X direction within the image field of the projection optical system 13 and is directed to the optical axis AX as an elongated strip-shaped spot light on the wafer. Projected onto W.

When the spot light and the wafer mark (diffraction grating mark) on the wafer W are moved relative to each other in the Y direction, the light generated from the wafer mark is transmitted through the projection optical system 13, the objective lens 50, etc. to the photoelectric detector. The light is received at 52. The photoelectric detector 52 has ± 1st order of the light from the wafer mark.
Only the third-order diffracted light is photoelectrically converted, and the photoelectric signal SDi corresponding to the light intensity obtained by photoelectrically converting in this manner is used as the main control system
It is output to the LSA calculation unit 57 in the inside. The LSA arithmetic unit 57 has a position signal PDs from the laser interferometer 15.
Also, the LSA calculation unit 57 samples the photoelectric signal SDi in synchronization with the up / down pulse generated for each unit movement amount of the wafer stage WS. Furthermore, LS
The A calculation unit 57 converts each sampling value into a digital value and stores it in the memory in the order of addresses, then calculates the position of the wafer mark in the Y direction by a predetermined calculation process, and stores this information in the alignment data storage of FIG. It is output to the unit 61.

Next, the structure of the main control system 18 shown in FIG. 2 will be described with reference to FIG. FIG. 4 shows the main control system 18 of this example and the members related thereto. In FIG.
Arithmetic unit 57, LIA arithmetic unit 58, FIA arithmetic unit 59, alignment data storage unit 61, EG
A calculation unit 62, storage unit 63, shot map data unit 64, system controller 65, wafer stage controller 66, and reticle stage controller 6
A main control system 18 is composed of 7. Among these members, the LSA arithmetic unit 57 and the LIA arithmetic unit 5
8 and the FIA arithmetic unit 59 obtains the coordinate position of each wafer mark in the stage coordinate system (X, Y) from the supplied photoelectric signal, and supplies the obtained coordinate position to the alignment data storage unit 61. Information on the measured coordinate position of the alignment data storage unit 61 is supplied to the EGA arithmetic unit 62.

The shot map data storage unit 64 stores the designed array coordinate values of the wafer marks belonging to each exposure shot on the wafer W in the coordinate system (x, y) on the wafer W. The array coordinate value of is also supplied to the EGA calculation unit 62. Based on the measured coordinate values and the designed coordinate values, the EGA calculation unit 62 uses the least squares method to convert the designed array coordinate values in the coordinate system (x, y) on the wafer W into the stage coordinate system (X , Y) to obtain six conversion parameters (corresponding to the conversion parameters a to f of (Equation 1)) for calculating the calculated array coordinate value,
The conversion parameters a to f are supplied to the storage unit 63.

Further, the EGA arithmetic unit 62 uses the conversion parameters a to f stored in such a manner as the wafer W.
Calculate the calculated array coordinate value in the stage coordinate system (X, Y) from the designed array coordinate value in the above coordinate system (x, y),
The calculated array coordinate value is supplied to the system controller 65. In response to this, the system controller 65
2 drives the wafer stage WS of FIG. 2 via the motor 16 while monitoring the measurement value of the laser interferometer 15 via the wafer stage controller 66, thereby positioning each shot area on the wafer W and each shot area. Exposure to. The system controller 65 also controls the laser interferometer 11 via the reticle stage controller 67.
While monitoring the measured value of
The reticle stage RS is driven to adjust the position of the reticle R.

Next, with reference to the flow chart of FIG. 1, the operation of positioning each exposure shot of the wafer to be exposed in this example and projecting and exposing the pattern image of the reticle R on each exposure shot will be described. explain. First, the wafer W to be exposed is loaded on the wafer stage WS shown in FIG. FIG. 5A shows an array of exposure shots on the wafer W. In FIG. 5A, the wafer W1 is regularly arranged along the coordinate system (x, y) set on the wafer W1. Exposure shots ES1, ES2, ..., ESN are formed, and a chip pattern is formed on each exposure shot ESi by the steps up to that point. Also,
Each exposure shot ESi is separated by a street line having a predetermined width in the x direction and the y direction.
Wafer mark M in the X direction as an alignment mark at the center of the street line extending in the x direction close to i
xi is formed, and a wafer mark Myi in the Y direction is formed in the center of the street line extending in the y direction near each exposure shot ESi. The wafer mark Mxi for the X direction and the wafer mark Myi for the Y direction are formed by arranging three linear patterns at a predetermined pitch in the x direction and the y direction, respectively, and these patterns are concave or convex on the base of the wafer W. It is formed as a partial pattern.

Then, in step 101 of FIG.
As shown in FIG. 5A, nine sample shots SA1 to SA1 selected in advance from all the exposure shots of the wafer W
For SA9, the coordinates on the stage coordinate system (X, Y) are measured. Wafer marks for the X direction and the Y direction are also formed close to the sample shots SA1 to SA9, respectively. In this example, by measuring these positions, the coordinate positions of the sample shots SA1 to SA9 on the stage coordinate system (X, Y) are measured. Specifically, the image pickup signal of the wafer mark Mx1 belonging to the sample shot SA1 is transmitted through the image pickup device 34 shown in FIG.
The wafer mark MX1 is supplied to the IA calculation unit 59, and the FIA calculation unit 59 detects the position of the wafer mark MX1 in the X direction based on the set measurement parameters.

FIG. 6 shows a state of the wafer mark Mx1 imaged by the FIA system image pickup device 34 of FIG. 2, and an image pickup signal obtained at that time is supplied to the FIA operation unit 59 of FIG. As shown in FIG. 6, within the imaging visual field VSA of the image sensor 34, a wafer mark Mx1 having three linear patterns and an index mark FM1 formed on the index plate 30 of FIG. 2 so as to sandwich the wafer mark Mx1. , FM2 are arranged. The image sensor 34 electrically scans the images of the wafer mark Mx1 and the index marks FM1 and FM2 along the horizontal scanning line VL. At this time, since only one scanning line is disadvantageous in terms of SN ratio, it is possible to add and average the levels of the imaging signals obtained by a plurality of horizontal scanning lines within the imaging visual field VSA for each pixel in the horizontal direction. desirable. As a result, the position of the wafer mark Mx1 in the X direction is measured, and the sample shot SA is similarly measured by the FIA system for the Y direction.
The position of the wafer mark My1 belonging to 1 in the Y direction is measured.

FIG. 5 (b) shows another example of the wafer mark. In FIG. 5 (b), a wafer mark MAX formed of a diffraction grating pattern having a predetermined pitch with respect to the measurement direction X is formed. Has been done. This wafer mark M
In order to detect the position of Ax, the two laser beams BM ₁ and BM ₂ emitted from the LIA optical system 45 (see FIG. 3) in the alignment sensor 17 of FIG. Irradiate on. Its pitch in the X direction of the crossing angle and the wafer mark MAx is the laser beam BM ₁ -1 order diffracted light B ₁ from the wafer mark MAx by (-1) and the laser beam BM ₂ +1 order diffracted light B ₂ from the wafer mark MAx by (+) Is set to be parallel. The interference light of the -1st-order diffracted light B ₁ (-1) and the + _1st-order diffracted light B ₂ (+) is converted into a photoelectric signal SDw by the photoelectric detector 52 of FIG. 3, and this photoelectric signal SDw is supplied to the LIA operation unit 58. In the LIA arithmetic unit 58,
The amount of misalignment of the wafer mark MAx in the X direction is calculated from the phase difference between the photoelectric signal SR as the reference signal and the photoelectric signal SDw.

FIG. 5C shows still another example of the wafer mark. In FIG. 5C, the dot marks are arranged at a predetermined pitch in the Y direction perpendicular to the X direction which is the measurement direction. The wafer mark MBx is formed.
To detect the position of the wafer mark MBx, the LSA optical system 46 (see FIG. 3) in the alignment sensor 17 of FIG.
The laser beam emitted from the laser beam is emitted as slit-shaped spot light LXS that is long in the Y direction in the vicinity of the wafer mark MBx. When the wafer stage WS of FIG. 2 is driven and the wafer mark MBx is scanned with respect to the spot light LXS, in a range in which the spot light LXS scans the wafer mark MBx, the wafer mark MBx is moved in a predetermined direction from the wafer mark MBx. Diffracted light is emitted to. A photoelectric signal SDi obtained by photoelectrically converting the diffracted light by the photoelectric detector 52 of FIG. 3 is supplied to the LSA operation unit 57, and LS
The A calculation unit 57 obtains the position of the wafer mark MBx in the X direction based on the set measurement parameter. Similarly, the coordinate values of the other sample shots SA2 to SA9 in the stage coordinate system (X, Y) are measured, and these measured coordinate values are sent to the EGA operation unit 62 via the alignment data storage unit 61 of FIG. Supplied.

Next, at step 102, the non-linear error amount of each sample shot SA1 to SA9 is obtained. Therefore, the EGA calculation unit 62 uses, for example, a simple least squares method to calculate the values of the six conversion parameters a to f that satisfy (Equation 1) from the designed coordinate values of the wafer mark and the measured coordinate values. Ask for. That is, the measured coordinate value of the nth sample shot SAn on the stage coordinate system is (XM _n , YM _n ), and the coordinate value calculated from the designed coordinate value based on (Equation 1) is (X _n , Y _n ),
The residual error component is expressed by the following equation. However, in the example of FIG. 5A, the value of m is 9.

[0047]

[Equation 2]

Then, the values of the conversion parameters a to f of (Equation 1) are determined so that this residual error component is minimized.
This is a calculation called EGA calculation. Next, EGA
The arithmetic unit 62 uses the measured coordinate values (XM _n , YM
_n ) from the conversion parameters a to f thus obtained
All sample shots SAi (i = 1 to 9) by subtracting the calculated array coordinate values (X _n , Y _n ) calculated using
The non-linear error amount (Pi, Qi) of the array error of is calculated. These nonlinear error amounts are supplied to the storage unit 63 in FIG.

FIG. 7A is an exaggerated example of the non-linear error amount of the sample shots SA1 to SA9 of the wafer W of FIG. 5A. In FIG. 7A, the non-linear error amount of the sample shot SA1 is shown. The amount is represented by a non-linear error vector <D1>, and the starting point P1 of the non-linear error vector <D1> is the calculated coordinate value (coordinate value including the linear error amount) of the sample shot SA1 and the end point of the vector <D1>. P2 represents the measured coordinate value of the sample shot SA1. For the vector <D1>, <D1> =
(P1, Q1) holds. The non-linear error amounts of the other sample shots are also represented by the non-linear error vector.

Next, in step 103, it is checked whether or not there are sample jumps. for that reason,
An average value Pi ₀ of the X component and an average value Qi ₀ of the Y direction of the nonlinear error amount (Pi, Qi) of each sample shot SAi (i = 1 to 9) are obtained. And each sample shot S
For Ai, the deviation of the nonlinear error amount in the X direction (Pi-P
i ₀ ) and the deviation (Qi−Qi ₀ ) in the Y direction are obtained, and the absolute value of the deviation vector is {(Pi−Pi ₀ ) ² + (Qi
The one in which the value of −Qi ₀ ) ² } ^1/2 is larger than a predetermined allowable value is defined as a “jump shot”. Sample shot SA1
If there is no such jump shot in SA9, the operation moves to step 112 and the normal EGA is executed.
Method is used for alignment.

That is, by using the conversion parameters a to f obtained so as to minimize the residual error component of the above (Equation 2) and the designed array coordinates, the EGA arithmetic unit 62 (Equation 1). From this, the calculated array coordinates of each exposure shot ESi in FIG. 5A are obtained, and the array coordinates thus calculated are supplied to the system controller 65 in FIG. The baseline amount, which is the distance between the measurement center of the FIA, LIA, and LSA alignment sensors and the reference point in the exposure field of the projection optical system 13, is determined in advance. Therefore, the system controller 65 sequentially positions each exposure shot area ESi on the basis of the calculated coordinate values obtained by correcting the array amount calculated by the EGA calculation unit 62 with the baseline amount. The pattern image of the reticle R is exposed. Then, in step 113, the next wafer is exposed.

On the other hand, assuming that the absolute value of the deviation vector of the non-linear error vector <D7> of the seventh sample shot SA7 in FIG. 7A exceeds the permissible value, the operation proceeds from step 103 to step 104. Move to. Then, as shown in FIG. 7B, several samples around the skipped sample shot SA7 (8 in the example of FIG. 7B).
Exposure shot of a new sample shot SA71
~ Select SA78 and sample shots SA
The coordinate values of 71 to SA78 on the stage coordinate system (X, Y) are measured.

Then, in step 105, the degree of correlation between the non-linear error amount of the skipped sample shot SA7 and the non-linear error amount of the peripheral sample shots SA71 to SA78 is examined. As an example for examining such a degree of correlation, sample shots SA7i (i = 1 to 8) and S
From the coordinate values (XM _7i , YM _7i ) and (XM ₇ , YM ₇ ) measured in the A7 stage coordinate system (X, Y), the designed coordinate value and the conversion parameter a to be obtained in step 102
The coordinate value (X
_7i, by subtracting Y _7i) and the _{(X '7, Y' 7} ), obtaining the nonlinear error amounts of the alignment errors of the sample shots SA7i and SA7 (P7i, Q7i) and the (P'7, Q'7) . Here, the non-linear error amount (P'7, Q'7) of the jump sample shot SA7 is obtained in step 102 (P
7 and Q7) are slightly different, so we have re-acquired them.

Next, the average value P ₀ of the X direction component and the average value Q ₀ of the Y direction component of the nine nonlinear error amounts of the skipped sample shot SA7 and the peripheral sample shots SA71 to SA78 are obtained. And these average values (P
₀ , Q ₀ ) is subtracted from the non-linear error amount of the skipped sample shot SA7 and the peripheral sample shots SA71 to SA78 to obtain the deviation vector (P7i-P ₀ , Q7).
_{i-Q 0) (i =} 1~8) and (P'7-P _0, Q'7
-Q ₀ ) is calculated. The absolute values of these nine deviation vectors are referred to as “correlation degrees”, and when the nine correlation degrees are larger than a predetermined allowable value, a jump sample shot SA7 and surrounding sample shots SA
71 to SA78 are regarded as having no correlation.

Then, in step 106, these nine decorrelation degrees are compared with their respective allowable values, and
As shown in (a), when at least one of the decorrelation degrees is larger than the allowable value, skip sample shot SA7 and peripheral sample shots SA71 to S71
Since the non-linear distortion tendency is different from that of A78, that is, the measurement result of the jumping sample shot SA7 is determined to be a measurement error due to the influence of wafer mark collapse or the like, the operation proceeds to step 110. In FIG. 8 (a),
Non-linear error vector <D7> of jump sample shot SA7 and non-linear error vector <D71> around it
~ The tendency with <D78> is different.

In step 110, the EGA method is used to perform alignment by using the measurement results of eight sample shots obtained by removing the skipped sample shot SA7 from the sample shots SA1 to SA9 in FIG. 7A.
That is, the conversion parameter a of (Equation 1) is set so that the residual error component obtained by subtracting the residual error of the sample shot SA7 from the above-mentioned residual error component of (Equation 2) is minimized.
Determine the value of ~ f. Then, the conversion parameters a to f
Then, the array coordinate of each exposure shot ESi is calculated from the designed coordinate value, and the pattern image of the reticle R is exposed to each exposure shot ESi which is aligned based on this array coordinate. Then, in step 111, the next wafer is exposed.

When it is considered that the wafer W processing condition is good and the occurrence of the jump shot is not necessarily a measurement error due to the influence of the collapse of the wafer mark or the like, the jump sample shot SA7 is taken. The measurement result may be regarded as correct. At this time, in order to perform the exposure to the skipped sample shot SA7, the alignment may be performed based on the result of individually measuring the coordinate position by the die-by-die method. In addition, in order to perform the exposure to the skipped sample shot SA7, the weighted EGA method as described later is used to perform the exposure.
The alignment may be performed by increasing the weight of the sample shots around the.

Further, in step 106, as shown in FIG.
As shown in (b), when each of the nine decorrelation degrees is less than or equal to the allowable value, a jump sample shot SA
7 and the peripheral sample shots SA71 to SA78 have the same tendency of non-linear distortion, and the strain area SA surrounding the sample shots SA7 and SA71 to SA78.
Since it is considered that there is a local non-linear distortion in 70 (see FIG. 5A), the operation moves to step 107. In FIG. 8B, a sample shot S is skipped.
The tendency of the non-linear error vector <D7> of A7 and the non-linear error vectors <D71> to <D78> around it are almost equal.

Thus, the strained area SA7 on the wafer W is
When there is a local distortion at 0, the alignment of all the exposure shots ES1 to ESN on the wafer W is performed by the weighted EGA method. In this weighted EGA method,
For example, as shown in FIG. 9, when performing exposure on an arbitrary exposure shot ESi on the wafer W, nine sample shots SA1 to SA9 and eight sample shots SA71 are performed.
N out of 17 sample shots consisting of SA78
A weight W _in is assigned to each of the nth (n = 1 to 17) sample shots.

And those 17 sample shots
Measured coordinate value (XM_n, YM _n), Based on (Equation 1)
Calculated coordinate value (X_n, Y_n) And weight W_inFor
And the residual error component of the exposure shot ESi
Ei is defined as follows. The value of m is 17 in the following formula
is there.

[0061]

[Equation 3]

The values of the conversion parameters a to f are determined so that the residual error component Ei takes the minimum value, and these conversion parameters a to f and the designed arrangement coordinates of the exposure shot ESi are substituted into (Equation 1). Exposure shot ES
The calculated array coordinates of i are obtained, and the pattern image of the reticle R is exposed on the exposure shot ESi aligned based on the calculated array coordinates.

Next, a method for optimizing the weight W _in will be described. As an example, in this example, as shown in FIG. 9, the weight W _in given to the n-th sample shot in which the measurement result is used is set to the distance LKn from the exposure shot ESi to the n-th sample shot. Is determined as follows. However, the parameter Si is a parameter for changing the degree of weighting.

[0064]

[Equation 4]

As is clear from this equation, the exposure shot E
The shorter the distance LKn to Si is, the larger the weight W _in given to the measurement result becomes. In (Equation 4), when the value of the parameter Si becomes large, the result becomes close to the result obtained by the conventional EGA method, and when the value of the parameter Si becomes small, the die by
It is close to the result obtained by the die method. In this example, the parameter Si is the following ratio r for each exposure shot ESi.
Is set to be a predetermined value r ₀ or less.

[0066]

[Mathematical formula-see original document] r = (sum of weights W _in given to sample shots other than the distortion area SA70 when calculating the calculated array coordinates of each exposure shot in the distortion area SA70) /
(The sum of the weights W _in given to the sample shots in the distortion area SA70 when calculating the calculated array coordinates of each exposure shot in the distortion area SA70)

This is because when the exposure shot ESi in the strained area SA70 having the local distortion shown in FIG. 5A is exposed, the sample shot SA in the area other than the strained area 70 is relatively exposed. It means that a small weight is given. This corresponds to step 107 in FIG. When the exposure shot ESi in the area other than the distortion area SA70 is exposed, the weight of the sample shot in the distortion area SA70 is set smaller than that of the sample shot SA in the area other than the distortion area SA70. Exposure is performed by performing alignment by the EGA method.
This corresponds to step 108 in FIG. Then, in step 109, the next wafer is exposed.

The weight W of the above weighted EGA method is used.
Another method for optimizing _in is step 106 in FIG.
In FIG. 5, when it is found that there is a correlation between the skipped sample shot SA7 and the peripheral sample shots SA71 to 78, the coordinates of all the exposure shots ESi of the wafer W of FIG. The position may be measured and the non-linear error amount may be obtained for each. In this case, depending on the distribution of these nonlinear error amounts,
The weight W _in is defined. Further, the distribution of the weight W _in may be variously changed to obtain the array coordinates by the weighting EGA, and the weight W _in when the residual error component becomes the minimum may be used.

As in step 112 of FIG. 1, when there is no sample shot on the wafer W but there is nonlinear distortion, alignment may be performed by the weighted EGA method. In this case, the value of the parameter Si is commonly set to, for example, Si ₀ in the following equation. In this equation, D is a weighting parameter, and the operator sets the value of the weighting parameter D to a predetermined value, whereby the parameter Si ₀ and thus the weighting W _in are automatically determined.

[0070]

Si ₀ = D ² / (8 · log _e 10) The physical meaning of this weighting parameter D is the range of sample shots effective for calculating the coordinate position of each shot area on the wafer (hereinafter, It is simply called "zone").
That is, when the zone is large, the number of effective sample shots is large, and the result is close to the result obtained by the conventional EGA method. On the contrary, when the zone is small, the number of valid sample shots is small, and the result is close to the result obtained by the die-by-die method.

The equation for determining the common parameter Si ₀ is not limited to (Equation 6), and the following equation can be used, for example. However, the area of the wafer is A [mm ² ], the number of sample shots is m, and the correction coefficient (positive real number) is C.

[0072]

[Equation 7] Si ₀ = A / (m · C) This equation reflects the change in the wafer size (area) and the number of sample shots in the determination of the parameter Si, so that the correction coefficient C The optimum value does not fluctuate too much. When the correction coefficient C is small, the value of the parameter Si ₀ is large, which is close to the result obtained by the conventional EGA method, and when the correction coefficient C is large, the value of the parameter Si ₀ is small.
It is close to the result obtained by the die-by-die method.

However, steps 107 and 108 of the present embodiment.
Then, according to the nonlinear distortion amount on the wafer W, the parameter Si
The value of is changed for each exposure shot.
When setting the value of, the value of the reference may be increased or decreased with reference to the value of the parameter Si ₀ of (Equation 6) or (Equation 7), for example. Further, in the above embodiment, the parameter Si
Although the weight W _in is determined based on (Equation 4),
The weight W _in ′ calculated from the parameter Si by the following formula may be used. In this case, as shown in FIG. 10, the distance (radius) between the deformation center point of the wafer (for example, the point-symmetrical center of nonlinear distortion), for example, the wafer center and the exposure shot ESi on the wafer is set to LEi, and the wafer center is set. Between m and m (m = 17 in the example of FIG. 10) sample shots LW1 to L
Wm. Then, the distance LEi and the distances LW1 to LW
A weight W _in ′ defined by the following equation is given to each of the measurement results of m sample shots according to m.

[0074]

[Equation 8]

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

[0076]

According to the alignment method of the present invention, the non-linear error amount is obtained for the sample area selected from the substrate, and the non-linear error amount is compared with the peripheral non-linear error amount to determine the non-linear error amount. It is determined whether the large peculiar region (flying shot) is due to a measurement error or a part of the locally distorted region. Then, in the case of a measurement error, the measurement result is excluded to perform alignment, and in the case of a locally distorted region, alignment of this region is mainly performed based on the measurement result of the sample region of this region. I am trying. Therefore, even if there is a jump shot in the sample area on the substrate, there is an advantage that the alignment can be performed with high accuracy on the entire surface of the substrate.

[Brief description of drawings]

FIG. 1 is a flowchart showing an exposure method including an embodiment of a positioning method according to the present invention.

FIG. 2 is a configuration diagram showing a projection exposure apparatus to which the exposure method of FIG. 1 is applied.

FIG. 3 is a TTL alignment sensor 1 shown in FIG.
7 is a block diagram showing a detailed configuration of No. 7.

FIG. 4 is a block diagram showing a detailed configuration of a main control system 18 and the like in FIG.

5A is a plan view showing an arrangement of exposure shots on a wafer exposed in the embodiment, FIG. 5B is an explanatory view of a wafer mark detection method for LIA system, and FIG. 5C is for LSA system. FIG. 3 is an explanatory diagram of a wafer mark detection method of FIG.

FIG. 6 is a diagram showing an observation region of an image sensor of an FIA alignment sensor.

7A is a plan view showing a linear error vector of a sample shot of the wafer shown in FIG. 5A, and FIG.
It is the top view which notched one part which shows the sample shot newly set around the sample shot SA7 of (a).

FIG. 8A is a diagram showing a case where the non-linear error amount of the sample shot SA7 and the non-linear error amount of the surrounding sample shots have different tendencies, and FIG.
It is a figure which shows the case where the tendency of the nonlinear error amount of A7 and the nonlinear error amount of the sample shot of the circumference is substantially equal.

FIG. 9 is an explanatory diagram of a first setting method of a weight assigned to each sample shot when aligning an exposure shot ESi on a wafer.

FIG. 10 is an explanatory diagram of a second setting method of the weight assigned to each sample shot when the exposure shot ESi on the wafer is aligned.

[Explanation of symbols]

1 Mercury Lamp 3 Illumination Optical System 9 Main Condenser Lens R Reticle 13 Projection Optical System W Wafer WS Wafer Stage 15 Laser Interferometer 17 TTL Type Alignment Sensor 18 Main Control System ES1 to ESN Exposure Shots SA1 to SA9, SA71 to SA78 Sample Shots SA70 strain region Mx1 wafer mark in X direction My1 wafer mark in Y direction

Claims (1)

[Claims] 1. A plurality of processed regions arranged on the substrate based on arrangement coordinates on a sample coordinate system set on the substrate are defined in a stationary coordinate system that defines a moving position of the substrate. Upon aligning with respect to a predetermined processing position, the coordinate position of at least three preselected sample areas in the stationary coordinate system among the plurality of processing areas is measured, and the plurality of measured coordinates are measured. By statistically calculating the position, the array coordinates on the stationary coordinate system of each of the plurality of processed regions on the substrate are calculated, and the substrate according to the calculated array coordinates of each of the plurality of processed regions. A method of aligning each of the plurality of processed regions with respect to the processing position by controlling a moving position, wherein the sample region is arranged on the stationary coordinate system. A first step of measuring a coordinate position; a second step of obtaining a non-linear error amount of a coordinate position of each of the sample areas on the stationary coordinate system from the coordinate position measured in the first step; Third step of measuring the coordinate position on the stationary coordinate system of the processed area around the singular area in which the non-linear error amount of the sample area exceeds a predetermined allowable value, and the first step and the third step. From the coordinate position measured in the process,
A fourth step of obtaining a non-linear error amount of the processed region around the singular region, wherein the non-linear error amount of the processed region around the singular region is the same as the non-linear error amount of the singular region. In the case of, the array coordinates on the stationary coordinate system of each of the unique region and the processed region around the unique region are defined as the coordinate position of the unique region and the unique position of the unique region. It is calculated by statistically calculating the coordinate position of the peripheral processed region measured in the third step, and the non-linear error amount of the peripheral processed region of the unique region is different from the non-linear error amount of the specific region. In the case of a tendency, the processed area is obtained by statistically calculating the coordinate positions measured in the first step and the third step excluding the coordinate positions measured in the first step for the unique area. Alignment method and calculating the arrangement coordinates on each of said stationary coordinate system.