U.S. patent application number 09/901708 was filed with the patent office on 2001-12-06 for alignment method and apparatus therefor.
This patent application is currently assigned to Nikon Corporation. Invention is credited to Furukawa, Osamu, Kawakubo, Masaharu, Magome, Nobutaka, Tateno, Hiroki, Yasuda, Masahiko.
Application Number | 20010049589 09/901708 |
Document ID | / |
Family ID | 27563441 |
Filed Date | 2001-12-06 |
United States Patent
Application |
20010049589 |
Kind Code |
A1 |
Yasuda, Masahiko ; et
al. |
December 6, 2001 |
Alignment method and apparatus therefor
Abstract
A method of aligning each of a plurality of processing areas
arranged on a substrate with a predetermined transfer position in a
static coordinate system XY for defining a moving position of said
substrate, a pattern of a mask being transferred to each of the
plurality of processing areas, the method comprising the steps of:
wherein each of the plurality of processing areas has a specific
point and a plurality of marks for alignment arranged by a
predetermined positional relationship with respect to said specific
point; measuring coordinate positions of a predetermined number of
marks selected from several processing areas of the plurality of
processing areas on the static coordinate system XY; calculating a
plurality of parameters in a model equation expressing the
regularity of arrangement of the plurality of processing areas by
performing a statistic calculation by use with the measured
plurality of coordinate positions, arrangement coordinate values
upon the design of the specific points of the several processing
areas and relative arrangement coordinate values upon the design of
the selected marks of the several processing areas with respect to
corresponding the specific points on the several processing areas;
and determining coordinate positions of respective said specific
points of the plurality of processing areas on the static
coordinate system XY by using the calculated parameters.
Inventors: |
Yasuda, Masahiko;
(Kawasaki-shi, JP) ; Furukawa, Osamu; (Tokyo,
JP) ; Kawakubo, Masaharu; (Kawasaki-shi, JP) ;
Tateno, Hiroki; (Kawasaki-shi, JP) ; Magome,
Nobutaka; (Kawasaki-shi, JP) |
Correspondence
Address: |
Nelson H. Shapiro
Miles & Stockbridge P.C.
Suite 500
1751 Pinnacle Drive
McLean
VA
22102-3833
US
|
Assignee: |
Nikon Corporation
|
Family ID: |
27563441 |
Appl. No.: |
09/901708 |
Filed: |
July 11, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
09901708 |
Jul 11, 2001 |
|
|
|
09240599 |
Feb 1, 1999 |
|
|
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Current U.S.
Class: |
702/150 ;
702/152 |
Current CPC
Class: |
G03F 9/7003
20130101 |
Class at
Publication: |
702/150 ;
702/152 |
International
Class: |
G01C 009/00; G06F
015/00; G01C 017/00; G01C 019/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jan 21, 1993 |
JP |
5-008194 |
Jun 8, 1993 |
JP |
5-137642 |
Jun 11, 1993 |
JP |
5-140580 |
Jun 8, 1993 |
JP |
5-137913 |
Oct 21, 1993 |
JP |
5-263241 |
Dec 8, 1994 |
JP |
6-304525 |
Claims
What is claimed is:
1. A method of aligning each of a plurality of processing areas
arranged on a substrate with a predetermined transfer position in a
static coordinate system XY for defining a moving position of said
substrate, a pattern of a mask being transferred to each of said
plurality of processing areas, wherein each of said plurality of
processing areas has a plurality of positioning marks arranged by a
predetermined positional relationship with respect to a specific
point set in each of said plurality of processing areas, said
method comprising: (1) with respect to at least one substrate among
a first to (K-1)th substrates (integer: 2.ltoreq.K.ltoreq.N):
measuring a coordinate position of a positioning mark in said
static coordinate system XY in each of several processing areas out
of said plurality of processing areas on said substrate by first
and second alignment sensors; calculating parameters of a first
model equation expressing the regularity of arrangement of said
plurality of processing areas by performing a statistical
computation using first coordinate positions measured by said first
alignment sensor and second coordinate positions measured by said
second alignment sensor, and arrangement coordinates upon a design
of said specific point and relative arrangement coordinates upon a
design of said positioning mark for said specific point in said
several processing areas; and moving said substrate relative to
said mask based on coordinate positions of said plurality of
processing areas in said static coordinate system XY, determined in
accordance with said calculated parameters; and (2) with respect to
a K-th substrate and subsequent substrates: measuring coordinate
positions of a plurality of positioning marks on said substrate in
said static coordinate system XY by one of said first and second
alignment sensors; calculating parameters of a second model
equation expressing the regularity of arrangement of said plurality
of processing areas based on the coordinate positions measured by
said one alignment sensor; and moving said substrate relative to
said mask based on coordinate positions of said plurality of
processing areas in said static coordinate system XY, determined in
accordance with the parameters of said first model equation and the
parameters of said second model equation.
2. A method according to claim 1, wherein (1) with respect to said
at least one substrate: calculating and storing differences between
said parameters of said first model calculated by a first
statistical computation using said first coordinate positions and
said parameters of said first model calculated by a second
statistical computation using said second coordinate positions, (2)
with respect to said K-th substrate and subsequent substrates: at
least one of said parameters of said second model equation is
determined in accordance with said stored differences and said
coordinate positions measured by said one alignment sensor, and the
others of said parameters of said second model equation are
determined in accordance with said coordinate positions measured by
said one alignment sensor.
3. A method according to claim 1, further comprising: correcting at
least on of a relative rotation error between said mask pattern and
each of said processing areas and a relative configuration error
between said mask pattern and each of said processing areas based
on said stored parameters.
4. A method according to claim 1, further comprising: measuring
some of said plurality of positioning marks by the use of only one
of said two alignment sensors with respect to the K-th and
subsequent substrates, while measuring another some of said
plurality of positioning marks by the use of any alignment sensor;
and determining parameters based on results of these
measurements.
5. A method in which each of a plurality of shot areas
two-dimensionally arranged on each of N (integer: N.gtoreq.2)
substrates in accordance with an arrangement coordinate upon the
design on said substrate is to be aligned with a predetermined
reference position in a static coordinate system for defining a
moving position of said substrate, a coordinate position of each of
said plurality of shot areas in said static coordinate system is
calculated by measuring a coordinate position of a shot area
selected in advance out of said plurality of shot areas in said
static coordinate system and by performing a statistical
computation of said plurality of coordinate positions measured, and
each of said plurality of shot areas is aligned with said reference
position by controlling said moving position of said substrate in
accordance with said calculated coordinate positions, wherein:
prior to the alignment of each of the plurality of shot areas on a
k-th (integer: 2.ltoreq.k.ltoreq.N) and subsequent substrates with
said reference position in accordance with the coordinate positions
calculated by said statistical computation, one-dimensional or
two-dimensional position measurement is performed at a plurality of
points in each of the shot areas by the use of two alignment
sensors with respect to at least one of the first to the (k-1)th
substrates, and a difference between results of the statistical
computations of the coordinate positions measured by the respective
alignment sensors and a result of the statistical computation in a
shot area of the coordinate positions measured by said respective
alignment sensors is obtained and stored; and one-dimensional or
two-dimensional position measurement is performed at one point in
each of the shot areas by the use of only one of said two alignment
sensors when the k-th substrate or any substrate subsequent thereto
is aligned, and the already-stored difference between results of
the statistical computations of the coordinate positions measured
by said two alignment sensors and the already-stored result of the
statistical computation in said shot area of the coordinate
positions measured by said respective alignment sensors is
corrected, whereby alignment can be effected based on said
corrected results.
6. A method according to claim 5, comprising: performing
one-dimensional or two-dimensional position measurement at one
point in a shot area by the use of one of said two alignment
sensors when the k-th substrate or any substrate subsequent thereto
is aligned, and measuring a one-dimensional coordinate position to
a predetermined direction at a different point in said shot area by
the use of either of the alignment sensors; and correcting a result
obtained by performing statistical computation of a measurement
result at said one point in said shot area and a measurement result
at said different point by the use of the already-stored difference
between results of the statistical computations of the coordinate
positions measured by said two alignment sensors and the
already-stored result of the statistical computation of the
coordinate positions in said shot area measured by said two
alignment sensors, respectively, thereby effecting alignment based
on said corrected results.
7. A method of transferring a pattern of a mask onto each of a
plurality of areas on a substrate, comprising: measuring coordinate
positions, on a static coordinate system in which said substrate is
moved, of first marks on said substrate; determining parameters in
an equation to define arrangement and a formal feature of said
plurality of areas in accordance with said measured coordinate
positions, said formal feature including at least one of rotation,
size and shape of said plurality of areas; and relatively moving
said mask and said substrate in accordance with said parameters to
transfer said pattern onto said each area.
8. A method according to claim 7, further comprising: forming an
image of said pattern on said substrate through a projection
optical system; and relatively rotating said mask and said
substrate based on a rotation error, of said areas relative to said
formed image, determined in accordance with a part of said
parameters.
9. A method according to claim 7, further comprising: forming an
image of said pattern on said substrate through a projection
optical system; and adjusting an optical property of said
projection optical system based on a configuration error, of said
areas relative to said formed image, determined in accordance with
a part of said parameters.
10. A method according to claim 7, further comprising: measuring
coordinate positions on said static coordinate system, of a
plurality of second marks on said mask; and determining a parameter
in an equation to define arrangement of said plurality of second
marks in accordance with the measured coordinate positions, wherein
said mask and said substrate are relatively moved in accordance
with the determined parameter and said parameters.
11. A method according to claim 7, wherein said parameters being
calculated so that each of deviations between said measured
coordinate positions and coordinate positions determined by said
equation for each of said first marks is minimized.
12. A method according to claim 11, wherein coordinate positions on
said static coordinate system, of said plurality of areas are
determined in accordance with said equation of which said
parameters are calculated to relatively move said mask and said
substrate based on the determined coordinate positions.
13. A method according to claim 9, wherein said configuration error
includes a magnification error of said areas relative to said
formed image.
14. A method according to claim 2, wherein the others of said
parameters of said second model equation includes an offset, a
rotation and a rectangular degree of said substrate and a rotation
of said processing areas.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to an alignment method and an
apparatus for determining a model equation expressing the
regularity of arrangement of a plurality of processing areas on a
wafer by use with, e.g., a statistic technique in order to predict
an arrangement coordinate value of each of the processing areas
prior to aligning each of processing areas with a predetermined
position and more particularly to an alignment method and an
apparatus suitable for aligning a pattern of a mask or a reticle
with each of processing areas (shot areas) accurately.
[0003] 2. Related Background Art
[0004] In the photolithography process for manufacturing
semiconductor devices, liquid crystal display devices or the like,
there are used projection exposure apparatuses, which project a
pattern of a mask or a reticle (hereinafter referred to as the
reticle) to each of shot areas on a sensitive substrate via a
projection optical system. Recently, as such apparatuses, step and
repeat type exposure apparatuses, e.g., reduction projection type
exposure apparatuses (stepper) have been widely used, wherein the
sensitive substrate is disposed on a two-dimensionally movable
stage and the image of the pattern of the reticle is exposed on
each of the shot areas on the sensitive substrate successively and
repeatedly while the sensitive substrate is shifted (stepping) by
the stage.
[0005] For example, in forming the conductor device, a plurality of
circuit patterns are piled one over another on the sensitive
substrate with a sensitive material applied thereon. Therefore,
when exposing the circuit pattern on the first layer and
thereafter, the pattern image of the reticle for the next exposure
needs to be superposed accurately on the circuit pattern already
formed on the wafer. That is, the wafer needs to be aligned with
the reticle accuratly. The alignment method for the wafer in the
conventional stepper or the like is as follows (e.g., U.S. Pat.
Nos. 4,780,617 and 4,833,621).
[0006] A plurality of shot area are arranged regularly on the wafer
based on the predetermined alignment coordinate values and provided
with the respective chip patterns having marks for alignment
(alignment marks). However, when superposing another pattern on the
pattern formed previously, even though the wafer is subjected to
the stepping operation based on the predetermined arrangement
coordinate values, the sufficient alignment accuracy cannot be
necessarily obtained owing-to the following factors.
[0007] (1) the residual rotation error of the wafer: .theta.
[0008] (2) the rectangular degree error of the stage coordinate
system (or shot arrangement): W
[0009] (3) the linear expansion or contraction of the wafer:
R.sub.x, R.sub.y
[0010] (4) the offset (parallel movement) of the wafer (center
position): O.sub.X, O.sub.Y
[0011] As these four error amounts can be expressed by six
parameters, the transformation matrix A of 2 lines.times.2 rows
including elements expressed by four parameters among those and the
transformation matrix O of 2 lines.times.1 row including elements
of the offset (parallel movement) O.sub.X, O.sub.Y are considered.
And, the arrangement coordinate value upon the design (D.sub.Xn,
D.sub.Yn) (n=0, 1, 2, . . . ) of the shot areas on the wafer and
the arrangement coordinate values (F.sub.Xn, F.sub.Yn) for the
actual alignment by the step and repeat method are expressed by use
with the transformation materices A and O as follows: 1 [ F Xn F Yn
] = A [ D Xn D Yn ] + O ( 1 )
[0012] At this time, the least squares method is used to determine
the transformation matrices A and O such that the deviation between
the arrangement coordinate value (FM.sub.Xn, FM.sub.Yn) actually
measured from each of shot areas selected from the plurality of
shot areas and the arrangement coordinate value upon calculation
(F.sub.Xn, F.sub.Yn) calculated for each of the corresponding
selected shot areas. Conventionally, on the basis of the determined
transformation matrices A, O and the alignment coordinate upon the
design (D.sub.Xn, D.sub.Yn), the arrangement value upon calculation
(F.sub.Xn, F.sub.Yn) for the actual alignment position is
calculated and the positions of shot areas on the wafer is
determined based on the calculated arrangement coordinate value
(F.sub.Xn, F.sub.Yn).
[0013] However, even though the wafer is positioned in accordance
with the calculated alignment coordinate value upon calculation
(F.sub.Xn, F.sub.Yn), the sufficient alignment accuracy cannot be
necessarily obtained owing to the following factors.
[0014] (1) the residual rotation errors of the circuit patterns
(chip pattern) of the shot areas on the wafer: .theta.
[0015] (2) the rectangular degree error of the coordinate system
(chip pattern) on the wafer: w
[0016] (3) the linear expansion or contraction of the chip pattern
in the two rectangular directions: rx, ry
[0017] These are caused by the deviation or rotation of the reticle
from a predetermined position, the projection magnification error
of the projection optical system or the distortion of the
projection optical system when the chip pattern is first (first
layer) printed on each shot area on the wafer. Furthermore, these
factors are changed by the distortion occuring at the time of
processing the wafer.
[0018] Further, there is presented such a disadvantage that when a
reticle is rotated or translated, a pattern image of the reticle
and a chip pattern on a wafer cannot be precisely aligned with each
other. Accordingly, as proposed in U.S. Pat. No. 4,699,515 or U.S.
Pat. No. 4,052,603, two marks facing together on both sides of a
circuit pattern on a reticle are detected so as to obtain a
rotational error, and the reticle or a wafer is rotated so as to
make the rotational error zero. Further, as proposed in U.S. patent
application Ser. No. 093,725 (Jul. 20, 1993), marks on a reticle
are transferred onto a plurality of partial areas on a wafer,
respectively, and latent images formed on the partial areas are
detected so as to obtain positional deviations which are then added
to arrangement coordinates (F.sub.Xn, F.sub.Yn) in order to
position the wafer. However, the former method offers such a
problem that it is difficult to drive the rotational error into a
value below a predetermined allowable value due to an error in
depiction of the marks on the reticle. Further, the latter method
offers such a problem that exposure operation for forming the
latent images greatly lowers the through-put.
[0019] Further, another disadvantage occurs such that the pattern
image of the reticle cannot precisely be aligned with the chip
pattern on the wafer over their entire surfaces due to an error in
the projection magnification of the projection system. Accordingly,
as proposed, for example, in U.S. Pat. No. 4,629,313, projected
positions of a plurality of marks on a reticle exclusive for
measurement are detected in order to obtain a projection
magnification of a projection optical system. However, there is
preset a problem in which this method has to use the reticle
exclusive for measurement so that a relatively long time is
required for the measurement of the magnification, causing the
through-put to be greatly lowered, and further, it is difficult to
precisely measure the projection magnification due to an error in
the depiction of the reticle.
[0020] When the circuit patterns of the second and subsequent
layers are projection-exposed on the wafers by the use of a
projection exposure apparatus such as a stepper, as stated above,
it is required to perform alignment of each shot area in which the
circuit pattern has already formed on the wafer with a pattern
image of the reticle serving as a mask to be exposed, namely
alignment between the wafer and the reticle, with high accuracy. An
alignment apparatus for executing such alignment is mainly
comprised of an alignment sensor for generating a photoelectric
signal by detecting the position of an alignment mark (wafer mark)
attached in each shot area on the wafer, a signal processing system
for obtaining an amount of deviation of said wafer mark from its
original position by processing said photoelectric signal, and a
positioning mechanism for compensating the position of the wafer or
the reticle based on the obtained amount of deviation.
[0021] As a method for such alignment sensor, there are a TTR
(through-the-reticle) method for observing (detecting) an alignment
mark (a reticle mark) on the reticle at the same time through a
wafer mark and a projection optical system, a TTL
(through-the-lens) method for not detecting the reticle mark, but
detecting the wafer mark only through the projection optical
system, and an off-axis method for detecting the wafer mark only
through a detection system which is separated from the projection
optical system.
[0022] Among these methods, since the TTR method or the TTL method
is designed to detect the wafer mark through the projection optical
system, and which projection optical system is designed to have the
most satisfactory color aberration for an exposure light, a desired
light is a laser beam (monochromatic light) or a quasi
monochromatic light having a wavelength range on the same level as
that of the exposure light (e.g., bright line spectrum of g-ray,
i-ray, etc., of a mercury-arc lamp). Accordingly, as an alignment
sensor of the TTR method or the TTL method, a sensor using a laser
beam as detection light is mainly used, such as a laser step
alignment (hereinafter called the "LSA") sensor which relatively
scans a wafer mark in a dot-array pattern form and a laser beam to
be converged in a slit form and detects a diffracted light
generated in a predetermined direction so as to detect the position
of said wafer mark, or a laser interferometric alignment
(hereinafter called the "LIA") sensor which irradiates laser beams
from a plurality of directions to a wafer mark in the form of a
diffraction grating so as to detect the position of said wafer mark
from a phase of the interference lights of a plurality of
diffracted lights emitted to the same direction from said wafer
mark. An alignment sensor of the LSA method and that of the LIA
method are disclosed, for example, in U.S. Pat. No. 5,151,750.
[0023] On the other hand, in the off-axis method, since there is no
limitation by the projection optical system, any type of
illumination light to the wafer mark can be adopted. As a result,
the above-mentioned LSA alignment sensor or the LIA alignment
sensor can be used. Further, for the off-axis method, an alignment
sensor of an image processing system (hereinafter called the FIA
(Field Image Alignment) system) is used, by which a wafer mark is
illuminated having an illumination light (broad band light) with a
predetermined band range (e.g., range of 200 nm or around) from a
halogen lamp, or the like, and an image pick-up signal obtained by
image-picking the image of said wafer mark is image-processed to
obtain the position of the wafer mark.
[0024] As a method for performing alignment in each shot area on
the wafer by using any of the above-mentioned alignment
apparatuses, an alignment method disclosed in the above-mentioned
U.S. Pat. No. 4,780,617 is proposed.
[0025] Out of the alignment sensors as mentioned above, an
alignment sensor of the off-axis system and the FIA method uses an
illumination light having a wide hand range so that said sensor is
hardly influenced from a thin film interference on a photoresist
layer which is coated on the wafer and is hardly influenced from
asymmetric characteristics of the wafer mark conveniently. However,
according to the off-axis method, a measured position and an
exposure position is separated comparatively widely, which results
in a poor through-put (the number of wafers processed per unit
time).
[0026] On the other hand, when an alignment sensor of the TTL
system and the LIA method is used, a moving distance between the
measured position and the exposure position is short (the moving
distance in some cases is substantially zero) because of the TTL
system, which is advantageous in terms of a through-put. However,
when an alignment sensor of the LIA method or the LSA method is
used, errors may be generated in measurement results of a scaling
(a linear expansion or contraction of the entire wafer) and a
magnification of a chip pattern within a shot area, under the
influence of the asymmetric configuration generated on the surface
of the wafer mark formed, for example, by aluminum vapor deposition
on the wafer. Moreover, since the used light is a monochromatic
laser beam, the sensor may be influenced by the thin film
interference of the photoresist. There is a possibility that extent
of these influences differs one another for each lot due to an
ununiformity of the process so that it is inconveniently difficult
to compensate these influences only with the constants obtained in
advance.
[0027] Particularly, the alignment method disclosed in the
above-mentioned U.S. Pat. No. 4,780,617 is a method for improving
both an alignment accuracy and a through-put (the number of wafers
processed per unit time) so that it is desired to use an alignment
sensor which is very satisfactory in terms of both the accuracy and
the through-put. In addition, it is required not only to improve
the alignment accuracy in each shot area, but also to enhance a
superposition accuracy within each shot area.
SUMMARY OF THE INVENTION
[0028] It is therefore an object of the present invention to
provide an alignment method and an apparatus capable of aligning
each of processing areas on the wafer with a predetermined position
at high speed and with accuracy even though the processing areas on
the wafer are expanded, contracted or rotated.
[0029] It is another object of the present invention to provide an
alignment method and an apparatus capable of aligning a pattern of
the mask with each of the shot areas precisely when transferring
the pattern of the mask to each shot area on the wafer.
[0030] Then, in the present invention, each of a plurality of
processing areas on a substrate on which a pattern of a mask is
transferred is provided with a plurality of marks for alignment
arranged by a predetermined positional relationship with respect to
the corresponding specific points defined on the respective
processing areas and prior to aligning each of the processing areas
with a predetermined transfer position in a static coordinate
system for defining a moving position of the substrate, coordinate
positions of a predetermined number of marks selected from several
processing areas of the plurality of processing areas on the static
coordinate system. Further, the statistic calculation is performed
to obtain parameters in a model equation expressing the regularity
of arrangement of the plurality of processing areas by use with the
measured plurality of coordinate positions; the arrangement
coordinate values upon design of the specific points corresponding
to the respective several processing areas; and the relative
arrangement coordinate values upon the design of the selected marks
with respect to the respectively corresponding specific points on
the several processing areas. Then, the coordinate positions of the
plurality of processing areas on the static coordinate system is
determined by using the calculated parameters. Therefore, it is
possible to align the plurality of processing areas with the
transfer position accurately by moving the substrate in accordance
with the determined coordinate positions.
[0031] Further, at least one of a relative rotation error between
the pattern of the mask and the processing areas and a relative
configuration error between the pattern of the mask and the
processing areas (magnification error, distortion error) is
corrected. Therefore, the pattern of the mask can be aligned with
each of the processing areas on the wafer with high accuracy. Also,
when the parameters in the model equation include the information
such as the rotation error, the configuration error, e.g., the
directionally uniform magnification error, two-dimentional marks
are used for the marks for alignment and coordinate positions of at
least two marks in each of the several processing areas on the
static coordinate system is measured.
[0032] Thus, in the present invention, the fact that the plurality
of processing areas arranged on the substrate in accordance with
the predetermined arrangement coordinate system have the rotation
error or the configuration error is taken into consideration, there
is used the model equation including the parameters related to the
arrangement of the specific points on the processing areas on the
wafer and the parameters related to the rotation error, the
configuration or the like of the processing areas (chip patterns)
with respect to the specific points. That is, by using the
coordinate positions of the marks for alignment on the several
processing areas on the static coordinate system; the arrangement
coordinate values upon design of the specific points on the several
processing areas; and the relative arrangement coordinate values
upon the design of the selected marks on the several processing
areas with respect to the respectively corresponding specific
points on the several processing areas, the statistic calculation
is performed to calculate the parameters in the model equation
expressing the regularity of arrangement of the plurality of
processing areas. Then, the coordinate positions of the respective
processing areas on the wafer on the static coordinate system is
determined by use with the calculated parameters. Therefore, even
though the processing areas on the wafer have the rotation error,
the configuration error or the like, each of the processing areas
can be aligned with the predetermined position by shifting the
substrate in accordance with the previously determined coordinate
positions.
[0033] The parameters in the model equation include, in addition to
the parameters (e.g., the residual rotation error of the
arrangement coordinate system on the substrate with respect to the
static coordinate system: .theta., the rectangular degree error of
the arrangement coordinate system (shot arrangement) on the
substrate: .theta., the linear expansion or contraction of the
substrate R.sub.x, R.sub.y, the offset of the center position of
the substrate with respect to the static coordinate system:
O.sub.X, O.sub.Y: total=six parameters) related to the arrangement
of the respective specific points of the plurality of processing
areas on the substrate, at least one parameter (e.g., the residual
rotation error of the chip pattern with respect to the arrangement
coordinate system on the substrate (chip rotation): .theta., the
rectangular degree error of the chip pattern: w or the linear
expansion or contraction of the chip pattern rx, ry) related to the
processing areas (chip pattern) on the substrate. Consequently,
based on the parameters of the model equation, especially based on
the parameters related to the chip pattern, at least one of the
relative rotation error or configuration error (magnification
error, distortion error or the like) between the pattern of the
mask and the processing areas is corrected. Therefore, it is
possible to align the pattern of the mask with the respective
processing areas on the substrate accurately over the whole surface
thereof.
[0034] When using the model equation including six parameters
related to the arrangement of the processing areas (specific
points) and at least one parameter related to the chip pattern, at
least seven coordinate positions are needed at the statistic
calculation. If the marks for alignment arranged by a predetermined
positional relationship with respect to the respective specific
points are one-dimensional marks, the coordinate positions of seven
or more one-dimensional marks on the substrate on the static
coordinate system is measured. Also, when the marks for alignment
are two-dimensional marks, the coordinate positions of four or more
two-dimensional marks on the substrate on the static coordinate
system are measured, but in one of them it is sufficient to measure
either the X or Y directional element of its coordinate position.
Besides, among the six parameters related to the arrangement of the
processing areas (specific points), e.g., if the linear expansion
or contraction error (scaling of the substrate) R.sub.x, R.sub.y
are deemed to be R.sub.x=R.sub.y, the number of the parameters can
be reduced. In short, the number of parameters related to the
arrangement of the processing areas (specific points) is optional
in the present invention, but the model equation including at least
one parameter related to the chip pattern should be used.
[0035] Further, the alignment errors between the pattern of the
mask and the respective processing areas (chip pattern) on the
substrate are represented, except the offset errors, by four
parameters related to the chip pattern, that is, the chip rotation
.theta.; the rectangular degree error of the chip pattern: w; the X
and Y directional scaling error of the chip pattern: rx, ry.
Accordingly, when using the model equation including the six
parameters (.theta., W, R.sub.x, R.sub.y, O.sub.x, O.sub.y) related
to the arrangement of the chip pattern (specific points) and four
parameters (.theta., w, rx, ry) related to the chip pattern, at
least ten coordinate positions need to be obtained. In short, prior
to performing the statistic calculation, it is necessary to obtain
the coordinate positions of equal to or more than a total number of
the parameters related to the arrangement of the chip pattern
(specific points) and the parameters related to the chip pattern
all to be included in the model equaiton. When using the model
equation including the ten parameters (.theta., W, R.sub.x,
R.sub.y, O.sub.x, O.sub.y, .theta., w, rx, ry), it is desirable to
provide four two-dimensional marks for alignment on each of the
processing areas on the wafer. At this time, it is desirable to
provide the four two-dimensional marks on the respective four
corners in each of the processing areas.
[0036] Besides, among the four parameters related to the chip
pattern, the rectangular degree error w of the chip pattern may be
neglected. Also, the X and Y directional scalings rx, ry may be
deemed to be rx=ry (=M). Then, when the rectangular w or the
scaling errors rx, ry are deemed to be w=0 or rx=ry, the number of
the parameters related to the chip pattern becomes three. At this
time, when the six parameters related to the arrangement of the
chip pattern (specific points) are used, a total number of the
parameters to be included in the model equation becomes nine, so
that it is sufficient to obtain at least nine coordinate positions.
Also, when the rectangular degree error w and the scaling errors
rx, ry are set to be w=0 and rx=ry, the number of the parameters
related to the chip pattern becomes two. At this time, it is
sufficient to provide at least one two-dimensional marks and one
one-dimensional mark on each of the processing areas on the wafer.
Further, when all the six parameters related to the arrangement of
the chip pattern (specific points) are used, a total number of
parameters to be included in the model equation becomes eight, so
that it is sufficient to obtain at least eight coordinate
positions. At this time, it is sufficient to measure the respective
coordinate positions of at least four two-dimensional marks, but
the coordinate positions of a few of one-dimensional marks and the
coordinate positions of a few of two-dimensional marks may be
measured instead. Furthermore, the two-dimensional mark may be a
combination of two one-dimensional marks.
[0037] When performing alignment of the m-th (integer:
2.ltoreq.m.ltoreq.n) substrate among n (integer: n.gtoreq.2)
substrates, in accordance with differences between the measured
coordinate positions of the marks of the several processing areas
of at least one specified substrate among the first to (m-1)th
substrates and coordinate positions thereof calculated according to
the calculated error parameters A, B and O, among the plurality of
marks formed on the processing areas on the m-th substrate, the
number of marks to be used for measuring the coordinate positions
is increased or decreased with respect to the number of marks
measured on the several processing areas on the specified
substrate. When among the marks measured on the several processing
areas on the specified substrate, there is a mark in which the
deviation of the difference between the measured coordinate
position and the calculated coordinate position is larger than a
predetermined value, the mark with the large deviation may be
excluded from the marks to be measured on the m-th substrate.
[0038] Namely, in the present invention, as the plurality of marks
for alignment are provided on each of the shot areas on the
substrate, the number of marks to be measured among the plurality
of marks is optimized to improve the alignment accuracy and the
throughput. Therefore, for only the first substrate in a lot or
several substrates from the first substrate, the positions and the
number of processing areas to be used for measuring coordinate
positions, and the number (and positions) of marks for alignment to
be measured on those processing areas are preset. Further, from the
actual measurement result, the deviations of the differences
(nonlinear error amounts) between the coordinate positions of the
alignment marks and the calculated coordinate positions thereof are
obtained. When performing alignment of the m-th (m.gtoreq.2)
substrate in the lot, it is sufficient to obtain the deviations of
the linear error amounts with respect to at least one substrate
among first to (m-1)th substrates. And, marks in which the
deviation of the nonlinear error amount is larger than the
predetermined value are excluded when performing measurement for
the following substrate, whereby the number of alignment marks to
be measured is decreased. When there are too many marks in which
the deviation of the nonlinear error amount is larger than the
predetermined value, new marks to be measured is set. That is, the
number of processing areas to be used for measuring coordinate
positions is increased and/or the number of alignment marks to be
measured per processing area is increased.
[0039] Therefore, even though the plurality of marks for alignment
are provided on each of the shot areas on the wafer, the number of
marks for alignment to be measured can be optimized in accordance
with the variations of the measurement result of the marks.
Accordingly, while maintaining alignment accuracy on a high level,
the reduction of the throughput can be minimized. Also, in several
shot areas, the marks for alignment belonging to each of the
several shot areas are measured, that is, position measurement by
the use of the same shape marks is repeated a plurality of times,
so that mechanical or electrical random errors of a detecting
system can be reduced. Further, when marks in which the deviation
of the difference between the calculated coordinate position and
the measured coordinate position is larger than the predetermined
value are excluded from marks to be measured on the following
substrate, it is possible to perform alignment more accurately and
speedily, excluding the marks by which measurement repeatability is
bad.
[0040] Further, in the static coordinate system XY for prescribing
the moved position of the substrate, coordinate positions of the
images of a plurality of specific marks formed on a mask having a
pattern to be transferred onto the substrate, which are given the
projection coordinate system, are detected, and are statistically
computed in order to calculate parameters for a model equation
representing an arrangement of the images of the plurality of
specific marks on the static coordinate system XY. The mask and the
substrate are positionally aligned together with the use of these
parameters, and thereafter, the image of the pattern on the mask is
transferred onto the substrate.
[0041] In particular, in the case of calculating parameters for a
model equation exhibiting the regularity of the arrangement of a
plurality of areas on the substrate with the use of the
above-mentioned statistic computation, the coordinate positions, in
the static coordinate system, of a plurality of areas to be process
are preferably determined with the additional use of parameters
which are obtained by statistic computation of the projected
positions of the specific marks on the mask. It is noted that any
one of equation (1), and equations (10), (17) can be used as the
model equation exhibiting the regularity of the arrangement of the
plurality of area to be processed on the mask. Before the pattern
on the mask is transferred into an area to be processed on the
substrate, at least either one of relative errors in rotation and
shape between the image of the pattern on the mask and the area to
be processed on the substrate can be compensated for with the use
of the above-mentioned two parameters.
[0042] Further, the model equation which exhibits, in the static
coordinate system XY prescribing the moved position of the
substrate, the arrangement of the projected images of the plurality
of specific marks on the mask, that is, the equation for
transforming coordinate positions on a coordinate system (.xi.R,
.eta.R) prescribed on the mask into coordinate positions in the
static coordinate system XY, can be expressed by using six
parameters (transformation matrices A, O), similar to equation (1).
These six parameters includes an error in the rotation of the mask,
errors in the magnifications of the projected image of the mask
pattern in the directions X, Y (linear expansion and retraction),
an error in the orthogonal degree of the mask coordinate systems
(.xi.R, .eta.R), and offsets of the mask in the directions X, Y.
Accordingly, the model equation, that is, the six parameters are
determined with the use of a statistic technique (such as the least
square process), and the thus determined parameters are used to
compensate the position of the mask or the substrate in order to
enhance the accuracy of alignment between the mask and the
substrate.
[0043] Further, at least either one of an error in the relative
rotation between the mask and the substrate and an error in the
projecting magnification of the projection system is compensated
for. Accordingly, the magnification of a pattern image on a first
layer mask can be precisely set to a predetermined value (for
example, 1/5), and an error in the rotation of the chip pattern
formed on the substrate can be set substantially to zero. A
rotation on a layer subsequent to the second layer, an error in
relative rotation between the pattern image thereof and an area to
be processed on the substrate, and an error in magnification can be
set substantially to zero.
[0044] Further, in the case of calculating the parameters of the
model equation exhibiting the regularity of the arrangement of a
plurality of areas to be processed on the substrate with the use of
a statistic technique, an error in the rotation of the substrate
(and also a chip pattern), an error in magnification and the like
can be compensated for. Accordingly, with the use of the
above-mentioned six patterns, an error in the relative rotation
between the pattern image of the mask and the area to be processed
on the substrate and an error in magnification are compensated for,
so as to precisely align the pattern image with the area to be
processed over their entire surfaces.
[0045] It is still another object of the present invention to
provide an alignment method sensor which is excellent in terms of
an alignment accuracy, and a superposition accuracy within each
short area, as well as a through-put.
[0046] According to the present invention, prior to alignment in
each of a plurality of shot areas on any of the k-th (k is an
integer of 2 or more) and the subsequent substrates with a
reference position thereof in accordance with a coordinate position
which has been calculated by a statistic computation,
one-dimensional or two-dimensional position measurement is
performed at a plurality of points in a shot area by the use of two
alignment sensors for at least one of the first to the (k-1)th
substrates, and a differences in a result of the statistic
computation of a coordinate position measured by the two alignment
sensors and a result of the statistic computation in the shot area
of the coordinate position measured by the two alignment sensors
are stored. When alignment on any of the k-th and subsequent
substrates is performed, one-dimensional or two-dimensional
position measurement is performed at one point in the shot area
only by one of these-two alignment sensors, and a result which is
obtained from statistic computation of these results of measurement
is corrected by using the already-stored difference in the result
of the statistic computation of the coordinate position measured by
the respective alignment sensors and the already-stored result of
the statistic computation within the shot area of the coordinate
position measured by the respective alignment sensors, thereby
performing the alignment based on a result of this correction.
[0047] In this case, when the alignment on any of the k-th and
subsequent substrates is performed, one-dimensional or
two-dimensional position measurement may be performed at one point
in the shot area by the use of only one of the two alignment
sensors, and a one-dimensional coordinate position at another point
in the shot area to a predetermined direction may be measured by
any of the alignment sensors. Then, the result of measurement at
said one point in said shot area, and the result obtained by
statistically computing the result of measurement at the other
point may be corrected by using the already-stored difference in
the statistic computation of the coordinate position measured by
the two alignment sensors and the result of the statistic
computation in said shot area of the coordinate position measured
by the two alignment sensors, respectively. Then, alignment may be
performed based on a result of this compensation.
[0048] According to the present invention having such structure,
with respect to the first substrate in one lot which comprises N
substrates or first several (to the k-th) substrates, two types of
alignment sensors (e.g., an LIA type sensor of the TTL system and
an FIA type sensor of the off-axis system) are used to measure a
one-dimensional or two-dimensional position of a wafer mark at a
plurality of measuring points, respectively, in the same sample
shot. Then, alignment of the method of statistically processing a
result of this measurement is performed. Then, differences between
the sensors of each parameter value for performing a statistic
processing which is obtained for the two alignment sensors are
calculated and stored.
[0049] When any of the subsequent wafers is exposed, only an
alignment sensor, for example, of the LIA type, or the like, of the
TTL system capable of a high through-put is used to perform the
alignment disclosed in U.S. Pat. No. 4,780,617, and the parameters
(e.g., a scaling) which may generate predetermined deviations by
the LIA system, or the like, are corrected by the difference with
those by, for example, the FIA system which is already stored. With
respect to an in-shot parameter such as a magnification of a chip
pattern (shot magnification), an alignment sensor which is the most
suitable for process of said substrate (e.g., an FIA sensor for the
shot magnification, and an LIA sensor for the shot rotation) is
used for the measurement, and the already stored parameters are
used to effect exposure. Thus, it is possible to enhance an
alignment accuracy and a superposition accuracy in a shot area,
while maintaining a high through-put.
[0050] With respect to any substrate subsequent, for example, to
the k-th substrate, alignment is conducted by the method disclosed
in U.S. Pat. No. 4,780,617 by using basically only an alignment
sensor of the LIA system of the TTL method, for example, which
renders a high through-put. Components which are easily changed for
each wafer out of the parameters in a shot area (a shot
magnification, shot rotation, or the like) are determined on the
basis of a result which is obtained by actually performing
measurement at a few points by using an alignment sensor most
suitable out of the two alignment sensors. As a result, a
superposition accuracy between shot areas can be further enhanced
without lowering the through-put much.
BRIEF DESCRIPTION OF THE DRAWINGS
[0051] FIG. 1 is a flowchart illustrating alignment and exposure
operations according to a preferred embodiment of the present
invention;
[0052] FIG. 2 is a schematic diagram of a projection exposure
apparatus of the present invention;
[0053] FIG. 3 is an enlarged diagram of the index marks and the
image of the alignment mark on the index plate of FIG. 2;
[0054] FIG. 4A is a diagram illustrating an example of the
arrangement of shot areas on a wafer;
[0055] FIG. 4B is an enlarged diagram of a shot area of FIG.
4A;
[0056] FIG. 5A is a diagram illustrating an example of a wafer with
chip patterns having rotation and magnification errors;
[0057] FIG. 5B is expranatory diagram illustrating the condition of
the chip rotation;
[0058] FIG. 5C is expranatory diagram illustrating the condition of
the magnification error of a chip pattern;
[0059] FIGS. 6A to 6C are diagrams illustrating examples of
two-dimensional alignment marks;
[0060] FIGS. 7A and 7B are diagrams illustrating examples of
one-dimensional marks;
[0061] FIGS. 8A and 8B are diagrams illustrating an example of
selecting alignment marks according to a conventional EGA
method;
[0062] FIGS. 9A to 9C are explanatory diagrams illustrating an
example of selecting alignment marks according to the embodiment of
the present invention;
[0063] FIG. 10 is a diagram for explaining a principle of a first
weighted EGA method according to another preferred embodiment of
the present invention;
[0064] FIG. 11 is a diagram for explaining a principle of a second
weighted EGA method;
[0065] FIG. 12 is a flowchart illustrating alignment and exposure
operations according to a third embodiment of the present
invention;
[0066] FIG. 13 is a diagram illustrating four alignment marks on a
shot area to be used in the third embodiment;
[0067] FIGS. 14A and 14B are diagrams showing another examples of
alignment marks;
[0068] FIG. 15 is a flow-chart showing alignment operation and
exposure operation in a sixth embodiment of the present
invention;
[0069] FIG. 16A is a view illustrating a pattern arrangement of a
reticle used in the sixth embodiment, and FIG. 16B is a view
illustrating the structure of an alignment mark on the reticle;
[0070] FIG. 17 is a view illustrating a projected image of the
reticle shown in FIGS. 16A and 16B;
[0071] FIG. 18 is a flowchart illustrating an exposure operation
according to a seventh embodiment of the present invention;
[0072] FIG. 19 is a structural diagram illustrating an essential
portion of a projection exposure apparatus used in the seventh
embodiment;
[0073] FIG. 20A is an enlarged plan view illustrating a shot area
and a wafer mark on the wafer;
[0074] FIG. 20B is an enlarged plan view illustrating the wafer
mark;
[0075] FIG. 20C is a cross-sectional view of the wafer mark shown
in FIG. 20B;
[0076] FIG. 21 is a view illustrating an image observed by an
alignment sensor of the FIA method;
[0077] FIG. 22 is a diagram for explaining a principle of detection
by an alignment sensor of the LIA method; and
[0078] FIG. 23 is a plan view illustrating an arrangement of a
sample shot on the wafer W to be subjected to an exposure operation
in the seventh embodiment.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0079] Now, it will be described a first preferred embodiment of
the present invention with reference to FIG. 1. In this embodiment,
the present invention is applied to a projection exposure apparatus
(stepper) for transferring a pattern of a reticle on each shot area
of a sensitive substrate (wafer) by a step and repeat method. FIG.
1 is a flowchart illustrating an example of an exposure sequence of
this embodiment and FIG. 2 is a schematic diagram of a projection
exposure apparatus to be used in this embodiment.
[0080] In FIG. 2, exposure light IL emitted from an illumination
optical system 1 illuminates a reticle 2 with approximately uniform
luminous intensity. As is not illustrated, the illumination optical
system 1 has an exposure light source, a fly eye lens, an aperture
opening (a aperture), a reticle blind, a condenser lens or the like
and the exposure light IL is higher harmonic wave such as g-ray,
i-ray, KrF or ArF excimer laser or YAG laser. Especially, in the
case of the excimer laser, the inclination angle of the etalon for
selection of wavelengths is adjusted while in the case of YAG
laser, the wavelength of the laser emitted from a wavelength
variable laser constituting a higher harmonic generator is changed,
thereby enabling the wavelength of the exposure light IL to be
changed. Thus, the imaging optical characteristics (e.g.,
projection magnification) of a projection optical system 7 can be
finely regulated.
[0081] A reticle 2 is supported on a reticle stage 3, which can be
two-dimensionally shifted and slightly rotated on a base plate 4 by
a driver 5. Also, the reticle 2 can be shifted parallely in the
direction of the optical axis of the projection optical system 7 on
the reticle stage 3 and inclined with respect to the plane
perpendicular to the optical axis by a plurality of piezo-electric
elements, as disclosed in U.S. Pat. No. 5,117,255. Accordingly, it
is possible to finely regulate the imaging optical characteristics
such as distortion. The movement of the reticle stage 3 is
controlled via the driver 5 by a main controller 6 for controlling
the entire operations of the apparatus.
[0082] The exposure light IL passing through the reticle 2 enters
the projection optical system 7 and projects the image of the
pattern of the reticle on a wafer 8 by reducing the pattern of the
reticle 2 in the retio of 1 to 5. In this embodiment, the
projection optical system 7 is constituted of a plurality of
refractive elements (lens elements) and at least one lens element
close to the reticle 2 is held slightly movably by a lens barrel.
The wafer 8 is supported by a slightly rotatable wafer holder 9,
which is disposed on a wafer stage 10. As disclosed in U.S. Pat.
No. 4,770,531, the wafer stage 10 has a XY stage for moving
two-dimensionally in a plane (XY plane) perpendicular to the
optical axis of the projection optical system 7, a Z stage provided
on the XY stage for moving in a direction (Z direction) parallel to
the optical axis and a leveling stage provided on the Z stage for
inclining the wafer holder 9 with respect to the XY plane.
[0083] A photoelectric sensor PS is provided on the wafer holder 9
(or the topmost stage of the wafer stage 10). The photoelectric
sensor PS is composed of a slit plate formed therein an opening
having a shape and dimensions substantially identical with those of
a blight part of the projected image of an alignment mark on the
reticle 2, and a photoelectric detector below the slit plate and
adjacent to the latter, for receiving light transmitted through the
slit. Further, the outer surface of the slit plate is set at a
height substantially equal to that of the exposed surface (for
example the outer surface) of the wafer 8. The photoelectric sensor
PS delivers an output signal to the main control system. In this
embodiment, by driving the wafer stage 10 so as to move the
photoelectric sensor PS in a plane perpendicular to the optical
axis 7a of the projection optical system 7, the positions of
projected images of a plurality of alignment marks on the reticle 2
are measured. An example of the structure of the photoelectric
sensor PS is disclosed in U.S. Pat. No. 4,629,313, and accordingly,
detailed expression thereof is omitted.
[0084] A movable mirror 11 is secured to an end portion of the
wafer stage 10 and laser interferometers 12 are disposed so as to
face the movable mirror 11. Although illustrated simply in FIG. 2,
when a rectangular coordinate system in a plane perpendicular to
the optical axis of the projection optical system 7 has a
X-coordinate and a Y-coordinate. The movable mirror 11 is
constituted of a plane mirror having a reflecting surface
perpendicular to the X-coordinate and a plane mirror having a
reflecting surface perpendicular to the Y-coordinate. The laser
interferometers 12 are constructed of two sets of laser
interferbmeters for the X-coordinate for emitting laser beams to
the movable mirror 11 along the X-coordinate and a set of laser
interferometers for the Y-coordinate for emitting laser beams to
the movable mirror 11 along the Y-coordinate axis. The coordinate
positions of the wafer stage 10 in the X and Y coordinate direction
is regularly measured by a set of the laser interferometer for the
X-coordinate and the interferometer for the Y-coordinate. Thus
defined rectangular coordinate system (X, Y) will be hereinafter
referred to as the stage coordinate system or the static coordinate
system. The rotation amount (rotation angle) of the wafer stage 10
is measured by the differences of measured values of the two sets
of laser interferometers for the X-coordinate. The information of
the X and Y-coordinate values on static coordinate system XY and
the rotation angle measured by the interferometers 12 are supplied
to a coordinate measurement circuit 12a and the main controller 6.
The main controller 6 controls the positioning operation of the
wafer stage 10 via a driver 13 while monitoring the information. As
not illustrated in FIG. 2, an interferometer system identical to
those provided on the side of the wafer is provided on the side of
the reticle.
[0085] Further, there is provided an imaging optical
characteristics control device 14 for adjusting the imaging optical
characteristics (e.g., projection magnification, curvature of
field, distortion or the like), as described in, e.g., U.S. Pat.
No. 5,117,255. The imaging optical characteristics control device
14 moves, e.g., independently three sets of lens elements close to
the reticle 2 among the plurality of lens element constituting the
objection optical system 7, thereby adjusting the projection
magnification and the distortion. The imaging optical
characteristics may be adjusted by sealing a space between two lens
elements and changing its internal pressure, as disclosed in, e.g.,
U.S. Pat. Nos. 4,871,237 and 4,666,237. Further, both the above
lens moving method and the internal pressure changing method may be
used in the imaging optical characteristics control device 14. As
described above, it is possible to adjust the imaging optical
characteristics of the projection optical system 7 by providing the
imaging optical characteristics 14, shifting the wavelength of the
exposure light IL or moving the reticle 2 in this embodiment.
[0086] An off-access type alignment system 15 is disposed on a side
of the projection optical system 7. A light source 16 emits light
having a wavelength band so as not to expose the photoresist. The
light emitted from the light source 16 is incident on an area
including an alignment mark 29 on the wafer 8 via a collimator lens
17, a beam splitter 18, a mirror 19 and an object lens 20. In the
off-access system, it is preliminary measured a base line amount
corresponding to the distance between an optical axis 20a of the
object lens 20 and the optical axis 7a of the projection optical
system 7. The reflected light from the alignment mark 29 reaches an
index plate 22 via the object lens 20, the mirror 19, the beam
spritter 18 and a condensing lens 21. An image of the alignment
mark 29 is formed on the index plate 22. The light passing through
the index plate 22 is incident on a beam spritter 24 via a first
relay lens 23. The light passing through the beam spritter 24 is
focused on the pick-up surface of an image pick-up device (e.g., a
two-dimensional CCD) 26x by a second relay lens 25X for the
X-coordinate while the reflected light by the beam spritter 24 is
focused on the pick-up of an image pick-up device (e.g., a
two-dimensional CCD) 26Y by a second relay lens 25Y for the
Y-coordinate. Then, the image of the alignment mark 29 and the
images of index marks of the index plate 22 is formed on the
respective pick-up surfaces of the image pick-up devices 26X and
26Y. Respective image signals from the image pick-up devices 26X
and 26Y are supplied to the coordinate measurement circuit 12a.
[0087] FIG. 3 illustrates a pattern on the index plate 22. A
cross-shaped image 29P of the alignment mark 29 is formed on the
middle portion thereof. The XP and XY directions perpendicular to
respective linear pattern images 29XP and 29YP of the image 29P
correspond to the X and Y directions of the stage coordinate system
of the wafer stage 10 in FIG. 2. The linear pattern images 29XP and
29YP intersect at right angles. Two index marks 31A and 31B are
formed so as to sandwitch the alignment mark image 29P with respect
to the XP direction while two index marks 32A and 32B are formed so
as to sandwitch the alignment mark image 29P with respect to the YP
direction.
[0088] The index marks 31A, 31B and the linear pattern image 29XP
arranged in the XP direction in a detection area 33X are picked up
by the image pick-up device 26X of FIG. 2 while the index marks
32A, 32B and the linear pattern image 29 YP arranged in the YP
direction in a detection area 33 are picked up by the image pick-up
device 26Y of FIG. 2. Further, the scanning directions for reading
photoelectric convertion signals from pixels of the image pick-up
devices 26X and 26Y are set to be the XP and YP directions
respectively. By processing the image signals from the image
pick-up devices 26X and 26Y, it is possible to obtain the
positional deviations of the alignment mark image 29P in the XP and
YP directions thanks to the index marks 31A, 31B and the index
marks 32A, 32B. Accordingly, the coordinate measurement circuit 12a
obtains the coordinate position of the alignment mark 29 on the
stage coordinate system (X, Y) by the positional deviations between
the image of the alignment mark 29 on the wafer 8 and the index
marks of the index plate 22 and the measurement result of the laser
interferometers 12. Thus obtained coordinate value is sent to the
main controller 6.
[0089] Next, it will be described operations for performing
alignment between the pattern image of the reticle 2 and each shot
area on the wafer 8 and performing exposure on each shot area.
[0090] In FIG. 4A illustrating the wafer 8, a plurality of shot
areas 27-n (n=0, 1, 2, . . . ) are arranged along an arrangement
coordinate system (.alpha., .beta.) on the wafer 8 in a matrix-like
form. The shot area 27-n is formed with a chip pattern having been
formed under the previous exposure and development processes. In
FIG. 4A, the only five shot areas 27-1 to 27-5 are represented
among the plurality of shot areas.
[0091] A reference position (specific point) is defined in the shot
area 27-n. For example, if it is assumed that the reference
position is a reference point 28-n in the center of the shot area
27-n, the coordinate value upon the design of the reference point
28-n in the coordinate system (.alpha., .beta.) on the wafer 8 is
expressed by (C.sub.Xn, C.sub.Yn). Also, the shot area 27-n is
provided additionally with four marks for alignment 29-n, 30-n,
34-n and 35-n. In this case, when a coordinate system (x, y) for
each shot area is defined on the shot area 27-n as illustrated in
FIG. 4B, the coordinate values on the design of the alignment marks
29-n, 30-n, 34-n and 35-n on the coordinate system (x, y) are
represented by (S.sub.1Xn, S.sub.1Yn), (S.sub.2Xn, S.sub.2Yn),
(S.sub.3Xn, S.sub.3Yn) and (S.sub.4Xn, S.sub.4Yn).
[0092] Returning to FIG. 4A, the wafer 8 is disposed on the wafer
stage 10 of FIG. 2 and the image of the reticle is exposed
successively on each of the plurality of shot areas with the chip
patterns having been formed previously by the step and repeat
method. At this time, the relationship between the stage coordinate
system (X, Y) for regulating the movement of the wafer stage and
the coordinate system (.alpha., .beta.) of the wafer does not
necessarily correspond to that in the previous process. Therefore,
even though the coordinate value of the reference point 28-n on the
stage coordinate system (X, Y) is obtained from the coordinate
value upon the design (C.sub.Xn, C.sub.Yn) of the reference point
28-n of the shot area 27-n on the coordinate system (.alpha.,
.beta.) and the wafer is shifted on the basis of the obtained
coordinate values, each shot area 27-n might not be positioned
accurately. Then, in this embodiment, there is assumed that the
alignment error occurs due to the following four factors the same
as conventional.
[0093] [1] Rotation of the Wafer: This is expressed by the risidual
rotation error .THETA. of the coordinate system (.alpha., .beta.)
of the wafer with respect to the stage coordinate system (X,
Y).
[0094] [2] Rectangular Degree of the Stage Coordinate system (X,
Y): This is caused by the reason that the advancement of the wafer
stage 10 in the X and Y directions is not performed rectangularly
and expressed by the rectangular degree error W.
[0095] [3] Linear Expansion or Contraction (Wafer Scaling) of the
Wafer in the .alpha. and .beta. Directions in the Coordinate System
(.alpha., .beta.): This occurs during processing of the wafer 8.
The amount of expansion or contraction is expressed by a wafer
scaling Rx in the .alpha. direction or a wafer scaling Ry in the
.beta. direction. The wafer scaling Rx is a ratio of the actually
measured value of the distance between two points on the wafer 8 in
the .alpha. direction to the designed value thereof while the wafer
scaling Ry is a ratio of the actually measured value of the
distance between two points on the wafer 8 in the .beta. direction
to the designed value thereof.
[0096] [4] Offset of the Wafer Coordinate System (.alpha., .beta.)
with respect to the Stage Coordinate System (X, Y): This is caused
by the reason that the entire wafer 8 is slightly displaced with
respect to the wafer stage 10 and expressed by the offset amounts
O.sub.X and O.sub.Y.
[0097] When the above error factors [1] to [4] are added, the shot
area 27-n with the reference point 28-n of the coordinate value
upon design (C.sub.Xn, C.sub.Yn) needs to be positioned for an
exposure on the basis of the coordinate value (C'.sub.Xn,
C'.sub.Yn) on the stage coordinate system (X, Y). The coordinate
value (C'.sub.Xn, C'.sub.Yn) is obtained by the following equation:
2 [ C x n ' C y n ' ] = [ Rx 0 0 Ry ] [ cos - sin sin cos ] [ 1 -
tan W 0 1 ] [ C Xn C Yn ] + [ O x O Y ] ( 2 )
[0098] When the rectangular degree error W and the residual
rotation error .theta. are deemed to be extremelly small amounts,
the equation (2) is approximated to the following equation: 3 [ C
Xn ' C Yn ' ] = [ Rx - Rx ( W + ) Ry Ry ] [ C Xn C Yn ] + [ O X O Y
] ( 3 )
[0099] It has been so far described to position the reference
position of each shot area 27-n (reference point in the center of
each shot area) accurately. However, even though the reference
points of the shot areas are positioned accurately, the projected
image of the reticle is not necessarily superposed on the entire
chip pattern of each shot area precisely.
[0100] Next, the alignment errors in the respective shot areas will
be described. As described above, in FIG. 4B, the alignment marks
29-n, 30-n, 34-n and 35-n are formed on the coordinate values upon
the design (S.sub.1Xn, S.sub.1Yn) to (S.sub.4Xn, S.sub.4Yn) on the
coordinate system (x, y) on the shot area 27-n. In this embodiment,
it is assumed that the alignment errors in the respective shot
areas are induced by the following factors.
[0101] [5] Rotation of a Chip Pattern (Chip Rotation): This is
caused by the reason that, e.g., when exposing the image of the
reticle 2 on the wafer 8, the reticle 2 is rotated with respect to
the stage coordinate system (X, Y) or yawing is included in the
movement of the wafer stage 10, and expressed by the rotation error
.theta. with respect to the coordinate system (x, y) of each shot
area.
[0102] [6] Rectangular Degree Error of a Chip: This is caused due
to the distortion of the pattern itself on the reticle 2 or the
distortion of the projection optical system 7, e.g., at the time of
exposing the image of the reticle 2 on the wafer 8 and expressed by
the angle error w.
[0103] [7] Linear Expansion or Contraction of a Chip (Chip
Scaling): This is due to the projection magnification error at the
time of exposing the image of the reticle 2 on the wafer 8 or the
whole or partial expansion or contraction of the wafer 8 during
processing and expressed by the chip scaling rx in the x direction
and the chip scaling xy in the y direction. The chip scaling rx is
a ratio of the actually measured value of the distance between two
points in the x direction on the coordinate system (x, y) on each
shot area to the designed value thereof, while the chip scaling ry
is a ratio of the actual measured value of the distance between two
points in the y direction to the designed value.
[0104] FIG. 5A illustrates the wafer 8A having the chip pattern of
the shot area 27-n formed in the previous process, wherein the
rotation and magnification errors occur in the chip patterns. In
FIG. 5A, shot areas 36-6 to 36-10 as indicated by broken lines are
an example of shot areas where no rotation or magnification error
occurs. On the other hand, the rotation angle and the magnification
in the shot areas 27-6 to 27-10 on the wafer 8A are different from
those in the shot areas 36-6 to 36-10. These errors can be
separated into the chip rotation error as illustrated in FIG. 5B
and the chip scaling error as illustrated in FIG. 5C. In the case
of the chip rotation error, the shot area 27-n is inclined relative
to the shot area 36-n while in the case of the chip scaling error,
the magnification in the shot area 27-n is different from that in
the shot area 36-n.
[0105] However, it is to be noted that in FIGS. 5A to 5C, there is
no rectangular degree error w of the chip patterns and the chip
scaling in the x direction is equal to the chip scaling in the y
direction.
[0106] When the above error factors [5] to [7] are added, the
alignment marks 29-n, 30-n, 34-n, 35-n with the coordinate values
upon design (S.sub.NXn, S.sub.NYn) (n=n) need to be aligned
actually on the basis of the coordinate value (S'.sub.NXn,
S'.sub.NYn) on the coordinate system (x, y). The coordinate value
(S'.sub.NXn, S'.sub.NYn) is obtained by the following equation: 4 [
S nXn ' S nXn ' ] = [ rx 0 0 ry ] [ cos - sin sin cos ] [ 1 - tan w
0 1 ] [ S n Xn S n Yn ] ( 4 )
[0107] When the rectangular degree error w and the rotation error
.theta. are deemed to be extremely small, the equation (4) is
approximated to the following equation: 5 [ S n Xn ' S n Yn ' ] = [
Rx - Rx ( W + ) Ry Ry ] [ S n Xn S n Yn ] ( 5 )
[0108] Referring to FIG. 4B, the arrangement value of the reference
point 28-n of the shot area 27-n on the stage coordinate system (X,
Y) is (C.sub.Xn, C.sub.Yn), so that the coordinate value upon the
design (D.sub.NXn, D.sub.NYn) of a certain alignment mark (29-n or
30-n) on a certain shot area 27-n on the stage coordinate system
(X, Y) is obtained from the following equation. It is to be noted
that the alignment marks 29-n to 35-n are discriminated by the
value N (1 to 4). 6 [ D N Xn D N Yn ] = [ C Xn C Yn ] + [ S n Xn S
n Yn ] ( 6 )
[0109] Three errors [5] to [7] occur when a chip pattern is printed
on the layer of the wafer 8 which has the printed alignment marks
on the respective shot areas. Further, the errors [2]and [3] caused
by the processing of the wafer 8 need to be taken into
consideration additionally. Therefore, when the coordinate values
on the stage coordinate system (X, Y) where the alignment marks
29-n, 30-n, 34-n, 35-n, need to be actually positioned is
(F.sub.NXn, F.sub.NYn) (N=1 to 4), the coordinate value (F.sub.NXn,
F.sub.NYn) is expressed from the equations (3) and (5) by the
following equation: 7 [ F NXn F nYn ] = [ C Xn ' C Yn ' ] + [ S n
Xn ' S n Yn ' ] = [ Rx - Rx ( W + ) Ry Ry ] [ C Xn C Yn ] + [ O X O
Y ] + [ Rx - Rx ( W + ) Ry Ry ] [ S NXn S NYn ] ( 7 )
[0110] Next, in order to facilitate the application of the least
squares method in this embodiment, the wafer scaling Rx in the a
direction and the wafer scaling Ry in the .beta. direction in the
equation (7) are expressed by utilizing respective new parameters
rx and ry as the following equation (8). Similarly, the chip
scaling rx in the x direction and the chip scaling .GAMMA.y in the
.GAMMA.y direction in the equation (7) are expressed by utilizing
respective new parameters .gamma.x and .gamma.y.
Rx=1+.GAMMA.x, Ry=1+.GAMMA.y, rx=1+.gamma.x, ry=1+.gamma.y (8)
[0111] When the equation (7) is renewed by utilizing these new four
parameters .GAMMA.x, .GAMMA.y, .gamma.x and .gamma.y expressing new
amounts of linear expantion or contraction, the equation (7) is
approximated to the following equation: 8 [ F NXn F NYn ] = [ 1 + x
- ( W + ) 1 + y ] [ C Xn C Yn ] + [ 1 + x - ( w + ) 1 + y ] [ S NXn
S NYn ] + [ O X O Y ] ( 9 )
[0112] In the equation (9), when the two-dimensional vector is
deemed to be the matrix of 2 lines.times.1 row, the equation (9) is
rewritten by the coordinate transformation equation for use with
the following transformation matrices.
FNn=ACn+BS.sub.Nn+O (10)
[0113] The respective transformation matrices in the equation (10)
are defined as follows. 9 F = [ F NXn F NYn ] , A = [ 1 + x - ( W +
) 1 + y ] B = [ 1 + x - ( W - I - ) 1 + y ] , O = [ O O ] C n = [ C
Xn C Yn ] , S N = [ S N Xn S N Yn ] ( 11 )
[0114] That is, in the equation (10), the matrix F.sub.Nn of 2
lines.times.1 row is expressed by the sum of the matrix AC.sub.n,
the matrix BS.sub.Nn and the matrix O. The ten parameters (.THETA.,
w, .GAMMA.x (=Rx-1), .GAMMA.y, O.sub.X, O.sub.Y, .theta., w,
.gamma.x (=rx-1), .gamma.y) in the transformation matrices A, B and
O in the coordinate transformation equation (10) can be, e.g.,
obtained by the least squares method. In this embodiment, the
coordinate values upon calculation on the stage coordinate system
(X, Y) for respective shot areas, the chip rotation error and the
chip magnification error are determined on the basis of the
coordinate transformation equation (10). Then, after the chip
rotation error, the chip magnification error or the like are
corrected, the alignment between each shot area on the wafer 8 and
the reticle is performed. It does not necessarily need to apply the
least squares method to the equation (10) and the ten error
parameters may be obtained by the equation (7).
[0115] In this embodiment, as will be described later in detail,
alignment marks are selected from preliminarily selected shot areas
(sample shots) from all the shot areas on the wafer and the
coordinate positions of the selected alignment marks on the stage
coordinate system (X, Y) are measured. Then, the result of the
measurement is utilized for the equation (10) and the ten
parameters are obtained by the least squares method. Thereafter,
the arrangement coordinate values of respective shot areas are
calculated. Such a calculation wherein predetermined error
parameters (less than ten possible) are obtained from the result of
measurement of preliminarily selected alignment marks (sample
shots) is called the enhanced global alignment (hereinafter called
"EGA") calculation. The method of performing alignment based on the
calculation result is called the EGA method alignment.
[0116] Next, it will be described an example of alignment and
exposure operations based on the coordinate transformation equation
(10) with reference to the flowchart in FIG. 1. First, in the step
101, the wafer 8 is disposed on the wafer holder 9 of FIG. 2. The
chip patterns have been already formed on the respective shot areas
under the previous process. Further, as illustrated in FIG. 4B, the
four cross-shaped alignment marks 29-n, 30-n, 34-n and 35-n are
formed in the shot area 27-n. Also, the alignment of the reticle 2
has been already completed and the deviations of the reticle 2 in
the X, Y and rotation directions with respect to the rectangular
coordinate defined by the interferometer (not illustrated) are
approximately zero.
[0117] Next, in the step 102, the origin of the wafer 8 is set
(prealignment). Then, in the step 103, the off-access alignment
system 15 is utilized to measure the coordinate values (FM.sub.NXn,
FM.sub.NYn) of five or more alignment marks (29-n, 30-n, 34-n or
35-n) on the wafer on the stage coordinate system XY. One alignment
mark has two elements in X and Y directions. Therefore, when the
coordinate values of five or more alignment marks are measured, it
is possible to determine values of ten or more parameters.
[0118] In this embodiment, although the alignment marks need to be
selected from three or more shot areas 27-n, it does not
necessarily need to select four alignment marks from one shot area
27-n and one alignment mark (29-n, 30-n, 34-n or 35-n) may be
selected from one shot area 27-n.
[0119] In this case, the arrangement coordinate values upon the
design (C.sub.Xn, C.sub.Yn) on the coordinate system (.alpha.,
.beta.) on the wafer 8 for the reference points 28-n of a plurality
of shot areas 27-n selected on the wafer 8 and the coordinate
values (relative coordinate values) upon design (S.sub.NXn,
S.sub.Nyn) on the coordinate systems (x, y) on the respective shot
areas 27-n for the measured alignment marks are known in advance.
Then, in the step 104, the arrangement coordinate values upon
design (C.sub.Xn, C.sub.Yn) of the reference points of the shot
areas having the measured alignment marks and the relative
coordinate values upon design (S.sub.NXn, S.sub.NYn) of the
measured alignment marks relative to the corresponding reference
points are substituted for the right side of the equation (10) to
obtain the coordinate values upon calculation (F.sub.NXn,
F.sub.NYn) on the stage coordinate system (X, Y) wherein the
alignment marks need to be positioned.
[0120] Thereafter, ten error parameters (.THETA., W, .GAMMA.x,
.GAMMA.y, O.sub.X, O.sub.Y, .theta., w, .gamma.x, .gamma.y)
satisfying the equation (10) are obtained by the least squares
method. Concretely, the difference (E.sub.NXn, E.sub.NYn) between
the actually measured coordinate value (FM.sub.NXn, FM.sub.NYn) and
the coordinate value upon calculation (F.sub.NXn, F.sub.NYn) is
deemed to be the alignment error. Therefore,
E.sub.NXn=FM.sub.NXn-F.sub.NXn and E.sub.NYn=FM.sub.NYn-F.sub.NYn
are concluded. And, five sets or more of alignment errors, that is,
ten or more alignment errors are squared and added. The obtained
value is then partially differentiated sequentially by the
respective ten error parameters. Further, ten equations are formed
such that the partially differentiated values each equal to zero.
Thereafter, the simultaneous equation of the ten equations is
solved to obtain the ten error parameters. These are the EGA
calculation in this embodiment.
[0121] Next, in the step 105, the reticle 2 is rotated properly via
the reticle stage 3 of FIG. 2 or the wafer 8 is properly rotated
such that the rotation error .theta. of the chip pattern in the
transformation matrix B is corrected, thereby the rotation of the
chip pattern relative to the stage coordinate system (X, Y) is
corrected. It means that the reticle 2 or the wafer 8 is rotated in
accordance with the rotation error .theta. in the transformation
matrix B in the equation.
[0122] However, when the wafer 8 is rotated, the offset errors
(O.sub.X, O.sub.Y) of the wafer 8 might be-changed. Therefore,
after remeasuring the coordinate values of the alignment marks, the
error parameters need to be again obtained by performing the
conventional EGA calculation. Then, for example, when the wafer 8
is rotated at an angle .theta., the errors in the chip patterns are
not taken into consideration at this time as conventional and the
coordinate values of alignment marks of at least three shot areas
on the wafer on the stage coordinate system XY are measured again.
Based on the result of the measurement, six error parameters
(.THETA., W, Rx, Ry, O.sub.X, O.sub.Y) are determined. Further, the
arrangement coordinate values are determined by the determined
error parameters and the respective shot areas are aligned for
exposure based on the arrangement coordinate values.
[0123] Next, the rectangular degree error w of the chips cannot be
corrected strictly speaking, but may be minimized by properly
rotating the reticle 2 or the wafer 8. Therefore, it is possible to
determine the rotation amount of the reticle 2 or the wafer 8
optimumly such that the sum total of the absolute values of the
rotation error .THETA., the rotation error .theta. and the
rectangular degree error w is minimized.
[0124] Thereafter, in the step 106, the projection magnification of
the projection optical system 7 is adjusted via the imaging optical
characteristics control device so as to correct the chip scaling
error in the transformation matrix B in the equation (10). It means
that the projection magnification of the projection optical system
7 is adjusted in accordance with the chip scalings rx and ry in the
transformation matrix B.
[0125] Then, in the step 107, the transformation matrices A and O
including the error parameters obtained in the step 104 are
utilized as known from the following equation. And, the arrangement
coordinate value upon the design (C.sub.Xn, C.sub.Yn) of the
reference point 28-n of each shot area 27-n on the wafer 8 is
substituted for the following equation to obtain the arrangement
coordinate value (G.sub.Xn, G.sub.Yn) of the reference point 28-n
on the stage coordinate system (X, Y). However, as described above,
when the wafer 8 is rotated to correct the rotation error in the
step 105, the arrangement coordinate value upon calculation
(G.sub.Xn, G.sub.Yn) is obtained on the basis of the remeasured
coordinate values of the alignment marks. 10 [ G Xn G Yn ] = A [ C
Xn C Yn ] + O ( 12 )
[0126] Thereafter, in the step 108, each reference point 28-n of
the shot area 27-n on the wafer 8 is positioned in respective one
of predetermined position within the exposure field of the
projection optical system 7 of FIG. 2 sequentially based on the
obtained the arrangement coordinate value (G.sub.Xn, G.sub.Yn) and
the preliminarily obtained base line amount. Then, the pattern
image of the reticle 2 is exposed on the predetermined shot area
27-n. After the entire shot areas on the wafer 8 have been exposed,
the wafer 8 is subjected to the development process.
[0127] In this-embodiment, not only the transformation matrices A,
O but also the transformation matrix B consisting of the parameters
such as the chip rotation, the rectangular degree error of the
chips and the chip scalings is taken into consideration, so that
the influence of the expansion or contraction or the rotation of
the chip patterns of the respective shot areas are reduced to a
small degree and then it is possible to superpose the projected
image of the pattern of the reticle on each of the chip patterns of
the shot areas on the wafer with high accuracy.
[0128] In the above embodiment, as illustrated in FIG. 4B, there
are provided the cross-shaped alignment marks 29-n, 30-n, 34-n and
35-n by which positionings in the X and Y directions on the stage
coordinate system can be performed simultaneously. Also, two
alignment marks 29-n and 30-n are provided on the x-coordinate axis
of the coordinate system of each shot area while two alignment
marks 34-n and 35-n are provided on the y coordinate axis thereof.
However, it does not necessarily need to be so, e.g., if four
alignment marks are not arranged on one line. For example, the
alignment marks may be arranged on four corners of each shot area.
Also, each alignment mark may be formed on street line areas
between each shot areas. Further, one-dimensional alignment marks
for the X direction may be provided separately from one-dimensional
alignment marks for the Y direction, if the precaution is taken
against their arrangement.
[0129] However, if one-dimensional alignment marks (diffraction
grating mark or the like) for detecting positions only in the X or
Y direction are utilized instead of the cross-shaped alignment
marks capable of specifying two-dimensional positions, the
coordinate values of ten or more one-dimensional alignment marks
need to be actually measured in order to determine the values of
ten parameters.
[0130] In the above-described embodiment, in order to obtain the
rotation error .theta. of the chip rotation, the rectangular degree
error w of the chip and the chip scalings rx and ry, the four
two-dimensional alignment marks 29-n, 30-n, 34-n and 35-n are
provided on each shot area 27-n on the wafer 8. However, although
each offset (x and y directions) of the reference point of the shot
area 27-n is taken into consideration, the number of parameters
which need to be selected is six, so that only three
two-dimensional alignment marks (e.g., 29-n, 30-n and 34-n) may be
provided on each shot area 27-n. Thus, when utilizing
two-dimensional alignment marks, always two alignment marks are
selected. However, when utilizing one-dimensional alignment marks,
six alignment marks need to be formed on each shot area 27-n.
[0131] Also, in the above embodiment, the rotation of the reticle
(or wafer) and the magnification of the projection optical system
are corrected by utilizing the four parameters (the chip rotation
.theta., the rectangular degree error w, the chip scaling rx, the
chip scaling ry) related to the chip pattern. However, the rotation
of the reticle (or wafer) and the magnification of the projection
optical system does not necessarily need to be corrected and only
the respective positions of the shot areas may be adjusted in
accordance with the arrangement coordinate values obtained in the
above embodiment. At this time, the correction of the magnification
may not be performed by utilizing the parameters Rx and Ry (or
.GAMMA.x and .GAMMA.y) of the scalings concerning, e.g., the wafer.
Further, instead of obtaining the arrangement coordinate values of
the shot areas from the equation (12), they may be obtained from
the equation (7) or the equation (9).
[0132] Also, in the above embodiment, all the four parameters (the
chip rotation .theta., the rectangular degree error w, the chip
scaling rx (=1+.gamma.x), the chip scaling ry (=1+.gamma.y)
concerning the chip pattern, only one of these may be paid
attention to and the equation (7) (or the equation (9)) may be
utilized. Concretely, when paying attention to the rotation error
.theta. only, the rectangular degree error w and the chip scalings
rx and ry are assumed to be 0 and 1 respectively and the equation
(7) is utilized. When the chip scalings rx and ry are paid
attention to, it is assumed that rx=ry, i.e., the linear expansion
or contraction is uniform in the x and y directions and the
equation (7) may be utilized. In short, kinds or the number of
parameters to be selected from the four parameters should be
determined in accordance with, e.g., kinds (characteristics) of
wafers, the degree of transformation of chip patterns or the
like.
[0133] Besides, when the rectangular degree error w is assumed to
be 0 and the chip scalings are uniform in the X and Y directions
(i.e., rx=ry=M) among four parameters (the chip rotation .theta.,
the rectangular degree error w, the chip scaling rx, the chip
scaling ry), the equation (7) is simplified as follows: 11 [ F NXn
F NYn ] = [ Rx - Rx ( W + ) Ry Ry ] [ C Xn C Yn ] + [ O X O Y ] + [
M - M M M ] [ S NXn S NYn ] ( 13 )
[0134] When the directionally uniform chip scaling M is set to be
(1+.delta.M), the equation (8) is utilized and the slight amount is
neglected. And the equation (13) is approximated to the following
equation: 12 [ F NXn F NYn ] = [ 1 + x - ( W + ) 1 + y ] [ C Xn C
Yn ] + [ O X O Y ] + [ 1 + M - 1 + M ] [ S NXn S NYn ] ( 14 )
[0135] In the equation (14), there are two parameters concerning
the chip patterns, so that the offset is taken into consideration
and it is sufficient to provide only two two-dimensional alignment
marks 29-n and 30-n in FIG. 4B on each shot area 27-n on the wafer
8. Besides, there are eight parameters in all. Therefore, in order
to determine the values of these error parameters by utilizing the
least squares method in the equation (14), it is sufficient to
measure at least four two-dimensional alignment marks.
[0136] Now, a second preferred embodiment of the present invention
will be described. The difference to the first embodiment is only
the structure of a model equation for calculating the arrangement
coordinate value of each shot area (chip pattern) on the wafer.
[0137] Although the coordinate value (F.sub.NXn, F.sub.NYn) on the
stage coordinate system (X, Y) of the alignment marks is expressed
in the equation (7) in the first embodiment, in this embodiment,
the coordinate value (F.sub.NXn, F.sub.NYn) is expressed from the
equations (3) and (5), as follows: 13 [ F NXn F NYn ] = [ Rx - Rx (
W + ) Ry Ry ] { [ C Xn C Yn ] + [ S NXn ' S NYn ' ] } + [ O X O Y ]
( 15 )
[0138] When the equation (15) is rewritten by utilizing the four
parameters .GAMMA.X, .GAMMA.Y as expressed in the equation (8), it
becomes as follows: 14 [ F NXn F NYn ] = [ 1 + x - ( W + ) 1 + y ]
[ C Xn C Yn ] + [ 1 + x - ( w + ) 1 + y ] [ S NXn S NYn ] + [ O X O
Y ] ( 16 )
[0139] When the two-dimentional vector is deemed to be the matrix
of 2 lines.times.1 row, the equation (16) can be rewritten by the
coordinate transformation equation having the following
transformation matrices. The respective transformation matrices of
the equation (17) are defined by the equation (11) the same as in
the equation (10).
F.sub.Nn=A{C.sub.n+BS.sub.Nn}+O (17)
[0140] In this embodiment, the ten parameters in the transformation
matrices A, B, O in the coordinate transformation equation (17)
should be calculated by utilizing the statistic calculation (e.g.,
least squares method). In this embodiment, similarly to the first
embodiment, even though there exist the chip rotation .theta., the
rectangular degree error w and the chip scalings rx and ry, each
shot area on the wafer can be positioned to the predetermined
position with high accuracy, and the projected image of the pattern
of the reticle 2 can be precisely superposed on each shot area
(chip pattern).
[0141] As the coordinate transformation equation (10) is utilized
in the first embodiment, in the step 105, the reticle 2 or the
wafer 8 is rotated in accordance with the chip rotation .theta. in
the transformation matrix B in the equation (10). Thereby, the
relative rotation errors between the projected image of the pattern
of the reticle and each shot area (chip pattern) on the wafer are
corrected. On the other hand, as the coordinate transformation
equation (17) is utilized in this embodiment, the reticle 2 or the
wafer 8 needs to be rotated in accordance with the sum
(.THETA.+.theta.) of the wafer rotation .theta. in the
transformation matrix A and the chip rotation .theta. in the
transformation matrix B so as to correct the above-mentioned
relative rotation errors. This is caused by the difference between
the coordinate transformation equations (10) and (17). The
correction operation for the rectangular degree error w or the chip
scalings rx and ry in the transformation matrix B in the equation
(17) is the same as in the first embodiment.
[0142] Next, examples of actually usable alignment marks will be
described with reference to FIGS. 6A to 6C. First, as alignment
marks (two-dimensional marks) for indicating the two-dimensional
coordinate, there are an L-shaped, T-shaped or chevron-shaped mark
other than the cross-shaped alignment mark 29 (see FIG. 6A) used in
the above embodiments. When using the double luminous flux
interfering type or the laser step alignment type alignment system
as disclosed in U.S. Pat. No. 5,151,750, a two-dimensional grating
pattern 41 (see FIG. 6B) becomes the two-dimensional mark also.
And, when using the laser step alignment type or the image pick-up
type alignment system as in the above embodiments, an alignment
mark 43 having a line and space pattern 42X arranged in the X
direction and a line and space pattern 42Y arranged in the Y
direction so as to be adjacent to the pattern 42X becomes the
two-dimensional mark (see FIG. 6C) also.
[0143] When selecting one of these two dimensional marks, two data
respectively for X and Y coordinates can be obtained as the data
for calculating ten (or less) parameters in the equation (10) or
(17) by means of the least squares method. Accordingly, the
selection of one cross-shaped alignment mark (e.g., 29-1) in the
above embodiments is equivalent to the selection of two alignment
marks (one-dimensional mark) for indicating one dimensional
coordinate. However, even when selecting a two-dimensional mark,
only one coordinate data for the X-coordinate or the Y-coordinate
data may be used.
[0144] As the one-dimensional mark for indicating the X-coordinate
as illustrated in FIG. 7A, there is the line and space pattern (or
diffraction grating mark) 42X arranged at a constant pitch in the X
direction. Also, as the one-dimensional mark for indicating the
Y-coordinate, there is the line and space pattern (or diffraction
grating mark) 42Y arranged at a constant pitch in the Y direction,
as illustrated in FIG. 7B. Further, the two-dimensional grating
pattern 41 of FIG. 6B may be deemed to be a one-dimensional mark in
the X or Y direction.
[0145] Next, it will be described another example of selecting
sample shots and alignment marks in detail. In this case, the
exposure apparatus effects the EGA calculation on the condition
that the result of measurement of the alignment marks formed in the
previous exposure process is utilized. Therefore, the positions and
the number of alignment marks in each shot area upon the design are
identical in the respective shot areas.
[0146] First, in the conventional EGA type alignment method, as
disclosed in U.S. Pat. No. 4,780,617 wherein errors in the chip
patterns are not taken into account, there are six error parameters
(.theta., W, Rx, Ry, O.sub.X, O.sub.Y). Therefore, if
two-dimensional alignment marks are converted into one-dimensional
alignment marks, at least six alignment marks need to be measured.
That is, it is sufficient to measure the X and Y coordinate values
in each of at least three measuring points which are not positioned
in a common line on the wafer. At this time, it is not necessary to
measure both a one-dimensional mark in the X direction and a
one-dimensional mark in the Y direction on the same shot area. That
is, in two shot areas, a one-dimensional mark in the X direction on
the one shot area and a one-dimensional mark in the Y direction on
the other shot area can be measured separately.
[0147] FIGS. 8A and 8B illustrate such a method of selecting the
alignment marks. In respective shot areas 44A, 44B, . . . , there
are provided one-dimensional marks (hereinafter called "X marks")
42XA, 42XB, . . . , for indicating the coordinate in the X
direction and one-dimensional marks (hereinafter called "Y marks")
42YA, 42YB, . . . for indicating the coordinate in the Y direction
respectively. Then, in order to measure the coordinate values of
e.g., six alignment marks, as illustrated in FIG. 8A, first, the
Y-coordinate values of the Y marks 42YA, 42YB and 42YC of the three
shot areas 44A, 44B and 44C are measured. From the result of the
measurement, three parameters (.theta., Ry, O.sub.Y) are obtained.
Thereafter, as illustrated in FIG. 8B, the X-coordinate values of
the X marks 42XA, 42XB and 42XD of the three shot areas 44A, 44B
and 44D are measured. From the result of this measurement, three
parameters (W, Rx, O.sub.X) are obtained. In this case, the shot
area 44D used in FIG. 8B is different from the shot area 44C used
in FIG. 8A, which causes no convenience.
[0148] Besides, after X and Y marks in different shot areas are
measured, X-coordinate values and Y-coordinate values at
predetermined measuring points may be obtained by calculation and
the EGA calculation may be performed based on the obtained
coordinate values.
[0149] Next, with reference to FIGS. 9A to 9C, it will be described
a method of selecting alignment marks when obtaining predetermined
error parameters selected from the four error parameters (the chip
rotation .theta., the rectangular degree error w, the chip scaling
rx, the chip scaling ry), besides the conventional six error
parameters. Five cases for selection of the error parameters will
be described.
[0150] (1) Calculation of Chip Scaling ry (or .gamma.y) only:
[0151] There are seven parameters to be obtained, so the coordinate
values of at least three X marks and four Y marks need to be
measured. In this case, as illustrated in FIG. 9A, in addition to
an X mark 42X and a Y mark 42Y, a Y mark 46Y whose Y-coordinate
value is different from the Y mark 42Y needs to be provided for the
shot area 44. The condition of selecting the Y marks to be used for
the EGA calculation is to select a Y mark (e.g., 46Y) which is not
positioned on a line 45 passing the selected one Y mark 42Y and
parallel to the X-coordinate axis. However, two Y marks satisfying
the condition do not need to be on the same shot area.
[0152] Ordinary, the mark arrangement in FIG. 9A is not adopted and
two two-dimensional marks 47 and 48 are often provided on a street
line area adjacent to the shot area. In this case, there are two
ways for obtaining the coordinate values of two Y marks. In the
first way, the Y-coordinate values of two two-dimensional marks 47
in the same first shot area are obtained. In the other way, the
Y-coordinate value of the two-dimensional mark 47 in the first shot
area and the Y-coordinate value of the two-dimensional mark 47 in
the other shot area are obtained.
[0153] (2) Calculation of the Chip Rotation only:
[0154] In addition to at least three X marks and three Y marks, the
coordinate value of at least one X mark or one Y mark needs to be
measured. The condition of selecting the last X mark is, as
illustrated in FIG. 9C, to select an X mark 51 which is not
positioned on a line 50 passing the previously selected X mark 42X
and parallel to the X-coordinate axis. Also, when selecting a Y
mark instead of the X mark, a Y mark 51Y which is not positioned on
a line 49 passing the previously selected Y mark 42Y and parallel
to the Y-coordinate axis needs to be selected. Also, in this case,
two X marks (or Y marks) satisfying the above condition do not need
to be on the same shot area.
[0155] (3) Calculation of the Chip Scaling ry and the Chip Rotation
.theta.:
[0156] In addition to at least three X marks and three Y marks, two
Y marks (one of them may be an X mark) need to be selected. Besides
the above conditions (1) and (2) are satisfied, three marks which
are not positioned on the same line need to be selected.
[0157] (4) Calculation of the Chip Scaling rx (or .gamma.x)
only:
[0158] The coordinate values of at least four X marks and three Y
marks need to be measured. Similarly to the above case (1), the
condition of selecting the four X marks is to select two points
which will not be parallel to the Y-coordinate axis.
[0159] (5) Calculation of the Rectangular Degree Error w only:
[0160] In addition to at least three X marks and three Y marks,
e.g., one X mark needs to be selected. Similarly to the above case
(2), the condition of selecting the four X marks is to select two
points which will not be parallel to the X-coordinate axis.
[0161] (6) Calculation of the Chip Scaling rx and the Rectangular
Degree Error:
[0162] In addition to three X marks and three Y marks, two X marks
need to be selected. Similarly to the above cases (3) and (4), the
condition of selecting the four X marks is to select three points
which will not be positioned on the same line.
[0163] As described above, either of the coordinate values of the Y
mark and the X mark may be utilized to calculate the chip rotation
.theta.. Also, either of the coordinate values of the X mark and Y
mark may be utilized to calculate the rectangular degree error w.
However, in the case of the rectangular degree error w, the
equations (7) and (15) (or equations (9) and (16)) of the above
embodiment are expressed so as to use the X mark, so the X mark is
used in the above embodiment. Also, the selection of the alignment
marks will not be limited to the same shot area.
[0164] Further, e.g., when the rectangular degree error w of the
chip is deemed to be zero, the number of error parameters necessary
to be determined in the equation (10) or (17) is nine.
Consequently, the number of the parameters to be decided in the
step 104 of FIG. 1 is nine, so it is sufficient to measure the
coordinate values of only nine or more one-dimensional alignment
marks defining positions in the X or Y directions in the step
103.
[0165] Furthermore, when the rectangular degree error w of the chip
is deemed to be zero and the expansion or contraction of the chip
in the X and Y directions are deemed to be directionally uniform
(rx=ry), it is sufficient to provide two alignment marks (e.g.,
29-n and 30-n) in each shot area 27-n.
[0166] In this case, the number of parameters necessary to be
determined is eight, so it is sufficient to measure the coordinate
values of four or more two-dimensional alignment marks (or the
coordinate values of eight or more one-dimensional alignment marks)
in the step 103 of FIG. 1.
[0167] On the other hand, more than four alignment marks may be
provided in each shot area. In this case, the measurement errors at
the time of measuring the coordinate values of alignment marks are
averaged. Further, the influence of the deviations of the alignment
marks from the designed positions due to the distortion of the
projection optical system at the time of printing the first chip
pattern (first layer) are preferably averaged by increasing the
number of alignment marks.
[0168] Especially, when utilizing the TTL (through the lens) type
alignment system for performing alignment by directly observing or
detecting the alignment marks through a projection optical system,
the measurement errors of the coordinate values caused by the
projection optical system can be reduced by increasing the number
of alignment marks. Furthermore, when the number of alignment marks
in each shot area is increased so as to take their arrangement
positions into consideration, it is possible to obtain not only the
rotation and the linear expansion or contraction but also the
nonlinear distortion in the chip pattern.
[0169] For example, when providing three alignment marks in each
shot area along the X direction, the nonlinear distortion in the X
direction can be obtained. Thus, by increasing the number of
alignment marks, it is possible to detect distortion elements of
the chip patterns (parallel movement, rotation, magnification,
rectangular degree, trapezoid distortion, barrel distortion,
pincushion distortion) collectively. In short, as the number of
alignment marks is increased, the number of error parameters can be
increased, enabling the occurances of errors to be detected more
accurately.
[0170] The distances between the reference point 28-n of each
sample shot on the wafer and the alignment marks formed relatively
to the reference point 28-n are comparatively short. Therefore,
regarding four error parameters (.theta., w, rx, ry) among ten
error parameters, errors due to measurement repeatability are
liable to occur. In order to minimize such errors, it is necessary
to increase the number of sample shots and the number of alignment
marks to be measured, which but reduces the throughput. Then, in a
third embodiment of the present invention, the reduction of the
throughput is prevented and alignment accuracy is highly maintained
by the following sequence. The following method utilizes the fact
that wafers in the same lot have the same tendencies of linear and
nonlinear errors and distortions of chip patterns of shot areas
thereof.
[0171] The operations of alignment and exposure of this embodiment
based on the coordinate transformation (17) will be described with
reference to a flowchart in FIG. 12. First, in the step 201, a
first wafer 8 to be exposed is taken out of a predetermined lot and
loaded on the wafer holder 8. And, its origin is set
(prealignment). All shot areas on the wafer 8 have chip patterns
formed in the previous process. As shown in FIG. 13, four
cross-shaped alignment marks 29 (n, N) (N=1 to 4) are formed on
each shot area 27-n on the wafer 8. In this embodiment, the
alignment marks are formed in four corners of each shot area 27-n.
Also, the alignment of a reticle 2 has been finished and deviations
thereof in the X and Y directions with respect to the rectangular
coordinate system (X, Y) defined by the interferometers (not shown)
and the direction of rotation are approximately zero.
[0172] Next, in the step 202, by utilizing the alignment system 15
in FIG. 2, coordinate values (FM.sub.NXn, FM.sub.NYn) of all the
alignment marks 29 (n, N) of all the shot areas 27-n on the wafer 8
on the stage coordinate system (X, Y) are actually measured. This
means that all the shot areas on the wafer 8 are made to be sample
shots and all the alignment marks are subject to measurement.
However, it is not always necessary to make all the shot areas 27-n
be sample shots and the number of sample shots may be slightly
larger than that of sample shots selected conventionally. It is
necessary to measure coordinate values of at least five or more
two-dimensional alignment marks to determine values of ten or more
parameters.
[0173] In this case, the arrangement coordinate values upon the
design (C.sub.Xn, C.sub.Yn) of the reference points 28-n of the
shot areas 27-n on the coordinate system (.alpha., .beta.) on the
wafer 8 and the coordinate values (relative coordinate values) upon
the design (S.sub.NXn, S.sub.Nyn) of the measured alignment marks
on the coordinate systems (x, y) on the respective shot areas 27-n
are known beforehand. Then, in the step 203, the arrangement
coordinate values (C.sub.Xn, C.sub.Yn) upon the design of the
reference points of the shot areas including the measured alignment
marks and the relative coordinate values upon the design
(S.sub.NXn, S.sub.NYn) representing positions of the measured
alignment marks with respect to the corresponding reference points
are substituted into the right side of the equation (16) to obtain
coordinate values upon calculation (F.sub.NXn, F.sub.NYn) on the
stage coordinate system (X, Y) in which those alignment marks
should be located.
[0174] Then, ten error parameters (.THETA., W, .GAMMA.x, .GAMMA.y,
O.sub.X, O.sub.Y, .theta., w, .gamma.x, .gamma.y) satisfying the
transformation (17) are obtained by the least square method.
Specifically, the differences (E.sub.NXn, E.sub.NYn) between the
actually measured coordinate values (FM.sub.NXn, FM.sub.NYn) and
the respective coordinate values upon the calculation (F.sub.NXn,
F.sub.NYn) are considered as alignment errors. Accordingly,
E.sub.NXn=FM.sub.NXn-F.sub.N- Xn and E.sub.NYn=FM.sub.NYn-F.sub.NYn
hold. The alignment errors (E.sub.NXn, E.sub.NYn) of the measured
alignment marks are respectively squared and added. The obtained
value is partially differentiated sequentially by the ten error
parameters. Then, ten equations are established such that the
partially differentiated expressions become zero. Thereafter, the
simultaneous equation of the ten equations is solved to obtain the
ten error parameters.
[0175] Then, in the step 204, the rotation error of the chip
pattern with respect to the stage coordinate system (X, Y) is
corrected by properly rotating the reticle 2 via the reticle stage
2 in FIG. 2 or rotating the wafer 8 such that the residual rotation
error (wafer rotation) .THETA. of the wafer in the transformation
matrix A of the transformation (17) and the chip rotation .theta.
in the transformation matrix B thereof are corrected. This means
that the reticle 2 or the wafer 8 is rotated in accordance with the
sum (.THETA.+.theta.) of the residual rotation error .THETA.
constituting an element of the transformation matrix A of the
transformation (17) and the rotation error .theta. constituting an
element of the transformation matrix B thereof.
[0176] However, when the wafer 8 is rotated, there is a danger that
the offset error (O.sub.X, O.sub.Y) of the wafer 8 is changed.
Therefore, it is necessary to remeasure coordinate values of the
alignment marks and to reperform calculation (EGA calculation) for
obtaining parameters by the above-mentioned least square method,
thereby obtaining error parameters. Namely, when the wafer 8 is
rotated by the angle (.THETA.+.theta.), the above steps 202 and 203
need to be repeated. This also means checking whether the value of
a new residual rotation error .THETA. after the rotation of the
wafer 8 corresponds to the angle by which the wafer 6 is rotated in
the step 204. Strictly speaking, the rectangular error w of the
chip cannot be corrected, but can be limited to a small amount by
rotating the reticle 2 appropriately. Then, it is possible to
optimize the amount of rotation of the reticle 2 or the wafer 8
such that the sum of the absolute values of the rotation error
.THETA., the rotation error 0 and the rectangular degree error w is
minimized.
[0177] Next, the magnification of the projection optical system 7
in FIG. 2 is adjusted via the imaging optical characteristics
control device 14 such that the chip magnification error of the
transformation matrix B of the transformation 17 is corrected. This
means that the magnification of the projection optical system 7 is
adjusted in accordance with the chip scalings rx (=.gamma.x-1) and
ry (.gamma.y-1) constituting an element of the transformation
matrix B of the equation (11).
[0178] Thereafter, by utilizing the transformation matrices A and O
including elements consisting of the error parameters obtained in
the step 203 and substituting the arrangement coordinate values
upon the design (C.sub.Xn, C.sub.Yn) of the reference points 28-n
of the respective shot areas 27-n on the wafer 8 into the equation
(12), arrangement coordinate values upon calculation (G.sub.Xn,
G.sub.Yn) on the stage coordinate system (X, Y) are obtained.
[0179] Further, in the step 205, the ten error parameters obtained
in the step 203, the coordinate values upon the design of the
reference points of the shot areas and the coordinate values upon
the design of the alignment marks 29 (n, N) are substituted into
the transformation (17) to obtain coordinate values upon
calculation (F.sub.NXn, F.sub.NYn) of the alignment marks 29 (n,
N). The differences of the measured coordinate values (FM.sub.NXn,
FM.sub.NYn) of the alignment marks 29 (n, N) and the coordinate
values upon the calculation (F.sub.NXn, F.sub.NYn) are obtained as
nonlinear error amounts (.DELTA.NXn, .DELTA.NYn), which are stored
in a memory. It is to be noted that when the wafer 8 is rotated in
the step 204, nonlinear error amounts calculated based on the
result of the remeasurement are stored in the memory.
[0180] In the step 206, in accordance with the calculated
arrangement coordinate values (G.sub.Xn, G.sub.Yn) and the
preliminarily obtained base line amount, the reference points 28-n
of the shot areas 27-n are successively aligned with a
predetermined position within the exposure field of the projection
optical system 7 in FIG. 2 to expose the pattern of the reticle 2
to the respective shot areas 27-n. After the whole shot areas on
the wafer have been exposed, a second wafer is loaded on the wafer
holder 9 in FIG. 2.
[0181] Next, in the step 207, the pattern of the reticle is exposed
to each of shot areas of the second to Q-th (Q is an integer of 2
or more) wafers in a similar manner to the first wafer. At this
time, for the alignment marks 29 (n, N) of the shot areas 27-n on
the respective first to Q-th wafers, nonlinear error amounts
(.DELTA..sub.NXn, .DELTA..sub.NYn) which are the differences
between measured coordinate values (FM.sub.NXn, FM.sub.NYn) and
calculated coordinate values (F.sub.NXn, F.sub.NYn) are obtained.
Further, for all the first to Q-th wafers, the average value
(.DELTA..sub.NXn, .DELTA..sub.NYn) and standard deviations
(.sigma..sub.NXn, .sigma..sub.NYn) of the nonlinear error amounts
(.DELTA..sub.NXn, .DELTA..sub.NYn) of the alignment marks 29 (n, N)
are obtained. In this embodiment, a shot area in which the sum of
the standard deviations (.sigma..sub.NXn, .sigma..sub.NYn) of the
alignment marks thereof is larger than a predetermined value is
excluded from the sample shots.
[0182] In the step 208, the initial value of a variable q is set to
be 1, and in the step 209, a (Q+q)-th wafer is loaded on the wafer
holder 9. In the step 210, among all alignment marks of all shot
areas on the wafer, shot areas in which the sum of the standard
deviations (.sigma..sub.NXn, .sigma..sub.NYn) of the alignment
marks thereof is larger than the predetermined value is excluded
from the sample shots and coordinate values of alignment marks of
left sample shots on the stage coordinate system (X, Y) are
measured. In the step 211, the (Q+q)-th wafer is exposed in the
same procedure as in the steps 203 to 206. At this time, the
measurement result of the alignment marks to be used to obtain ten
error parameters correspondingly to the step 203 are the
measurement result of the alignment marks actually measured in the
step 210. In the step 212, the average value (.DELTA..sub.NXn,
.DELTA..sub.NYn) and standard deviations (.sigma..sub.NXn,
.sigma..sub.NYn) of nonlinear error amounts (.DELTA..sub.NXn,
.DELTA..sub.NYn) of the alignment marks of the (Q+q) wafer measured
in the step 210 are obtained.
[0183] In the step 213, it is checked whether a wafer to be exposed
is left in the lot. When there is a wafer to be exposed, the value
of the variable q is increased by one in the step 214 and the
procedure goes back to the step 209. When there is no wafer to be
exposed, the whole operation is finished. In this case, as the
number of exposed wafers in the lot increases, the number of sample
shots to be measured decreases. When the number of sample shots to
be measured becomes approximately equivalent to that of sample
shots used in the ordinary EGA method, the number of sample shots
and the positions thereof are fixed. Thereby, while the alignment
accuracy is maintained with high accuracy, reduction of the
throughput of the exposure process can be prevented.
[0184] Instead of decreasing the number of shot areas in the step
210, the number of alignment marks on the sample shots to be
measured may be decreased. In this case, as exposures to the wafers
in the lot progress, the number of sample shots decreases and the
number of alignment marks on the sample shots as well as the
arrangement thereof are changed. However, when, e.g., alignment
marks in the four corners of a sample shot are measured, there is a
case that only the standard deviation of the alignment mark in one
corner (e.g., only 29 (n, N) in FIG. 13) becomes large. In this
case, only that alignment mark may not be measured. But,
independently of that, alignment marks to be measured may be
decreased uniformly from alignment marks in four corners on sample
shots. For decreasing alignment marks uniformly, it is preferable
to decrease first an alignment mark having the much larger standard
deviation of the nonlinear error amount for each corner (e.g., for
each alignment mark 29 (n, N)). Also, there is a method not that
the number of sample shots is determined to be large and all
alignment marks thereof are measured but that about one or two
alignment marks for each sample shot are measured uniformly.
[0185] Further, for increasing or decreasing alignment marks in
this embodiment, there is another method in which alignment marks
to be measured are selected so as to be arranged constantly
uniformly (approximately uniform density distribution) on the
entire surface of a wafer, and their density is changed by the
increase or decrease of the number of alignment marks. That is, for
example, a method can be considered in which the entire surface of
a wafer is divided into a plurality of blocks in the shape of a
grating and first it is set that the respective blocks have the
same number of alignment marks to be measured. Thereafter, the
number of alignment marks in each block is decreased or increased
by the same rate in accordance with nonlinear error amounts of
measurement results. Such a method is advantageous in that the
measurement information of alignment marks can be obtained
approximately uniformly over the entire surface of the wafer.
[0186] Also, in the alignment of the conventional EGA method in
which the number of error parameters (.THETA., W, Rx, Ry, O.sub.X,
O.sub.Y) is six, without lowering the throughput and the alignment
accuracy, the number of alignment marks to be measured can be
optimized by increasing or decreasing the number of alignment marks
to be measured in accordance with nonlinear error amounts of
measured alignment marks.
[0187] In this embodiment, as shown in FIG. 13, the four
cross-shaped two dimensional alignment marks 29 (n, N) by which
alignment can be performed simultaneously in the X and Y directions
on the stage coordinate system are formed in the respective four
corners on the diagonal lines of the shot area 27-n. However, it is
not always necessary to take such a way if four alignment marks are
not arranged on a line. Also, it is not always need to form
alignment marks within the shot area 27-n. For example, four
alignment marks 29 (n, 1) to 29 (n, 4) may be formed in the centers
of sides of a street line area between the shot area 27-n and
adjacent shot areas.
[0188] Also, the number of alignment marks 29 (n, N) on the shot
area 27-n may be less than four. For example, as shown in FIG. 14B,
two alignment marks 29 (n, 1) and 29 (n, 2) may be formed on a
diagonal line of a street line area 37 surrounding the shot area
27-n. In this case, alignment marks 29 (n-1, 1) and 29 (m, 1)
belonging to other shot areas are formed at other positions of the
street line area 37.
[0189] Also, one-dimensional alignment marks for the X direction
and one-dimensional alignment marks for the Y direction may be
separately provided to obtain the transformation matrices A, B and
O of the equations (10) and (17) if precaution is taken with their
arrangement. Specifically, as shown in FIG. 14A, alignment marks
35x and 36x indicating positions in the X direction and alignment
marks 35y and 36y indicating positions in the Y direction may be
formed in the four corners of the shot area 27-n. However, when
using one-dimensional alignment marks capable of specifying
positions in the X or Y direction as shown in FIG. 14A instead of
cross-shaped alignment marks capable of specifying two-dimensional
positions as shown in FIG. 13, it is required to measure coordinate
positions of ten or more alignment marks to determine ten
parameters. Further, there is a case that only at least one
parameter among the four parameters (.theta., w, rx, ry) may be
obtained in addition to the conventional six parameters (.THETA.,
W, Rx, Ry, O.sub.X, O.sub.Y). Thus, when obtaining seven parameters
in total, it is sufficient to measure coordinate values of seven or
more one-dimensional alignment marks.
[0190] Among the four parameters (.theta., w, rx, ry) related to
the chip pattern, if there are parameters (e.g., chip scalings rx
and ry) in which an average value of the measurement results of
several initial wafers is utilized, which will be described later
in detail, the number of unknown parameters is further reduced,
whereby the minimum number of alignment marks to be measured in the
step 210 is reduced. In short, when converted to one-dimensional
marks, it is sufficient to measure coordinate values of alignment
marks the number of which is at least the same as that of unknown
parameters.
[0191] Next, a fourth embodiment of the present invention will be
described. In this embodiment, the process of exposing a plurality
of wafers of a lot successively by the projection exposure
apparatus of FIG. 2 is changed from that in the third embodiment
and only the operation different from that in the third embodiment
will be described.
[0192] Also, in this embodiment, four alignment marks 29 (n, 1) to
29 (n, 4) as shown in FIG. 13 are formed on each of shot areas of
the wafers. When exposing the first to Q-th wafers in a similar
manner to the third embodiment, approximately all the shot areas on
each wafer are made to be sample shots and coordinate values of
four alignment marks on each sample shot on the stage coordinate
system (X, Y) are measured. From these measurement results, the
correction of chip rotation, etc. and exposure for each wafer are
performed in accordance with the steps 203, 204 and 206 in FIG.
12.
[0193] At this time, instead of obtaining a nonlinear error amount
of each alignment mark in the step 205, four error parameters
(rotation error .theta., rectangular degree error w, linear
expansion or contraction rx (=1+.gamma.x) and ry (=1+.gamma.y))
related to the chip pattern among ten error parameters (.THETA., W,
.GAMMA.x, .GAMMA.y, O.sub.X, O.sub.Y, .theta., w, .gamma.x,
.gamma.y) in the transformation (17) are stored in a memory. Next,
in a process corresponding to the step 207 of FIG. 12, the
respective average values of the four error parameters (.theta., w,
rx, ry) related to the chip patterns in the first to Q-th wafers
are obtained. Thereafter, when exposing left wafers, corrections of
the chip rotation, the rectangular degree of the chip and the
expansion or contraction of the chip are performed by commonly
utilizing the average values of the four error parameters (.theta.,
w, rx, ry) obtained with respect to the first to Q-th wafers.
[0194] Among the average values of the four error parameters
(.theta., w, rx, ry) with respect to the first to Q-th wafers, the
average value of at least one error parameter (e.g., only the chip
scaling rx) may be commonly utilized, and the other error
parameters are obtained separately for each wafer. For example,
depending on lots, there is a case that tendencies of the chip
scalings rx and ry and the rectangular degree error w of the chip
are the same over whole wafers. In such a case, as to the chip
scalings rx and ry and the rectangular degree error w of the chip,
the average values of the measurement results of several initial
wafers in the lot may be utilized commonly. On the other hand, the
rotation error .theta. of the chip rotation is liable to be varied
for each wafer in the same lot, so is obtained for each wafer.
[0195] Accordingly, when exposing a (Q+1)-th wafer in the fourth
embodiment, the average values of the four error parameters
concerning the chip patterns are utilized, so that it is necessary
to determine only six error parameters (.THETA., W, Rx, Ry,
O.sub.X, O.sub.Y) similarly to the conventional EGA method. That
is, about ten shot areas are specified as sample shots in a similar
manner to the conventional EGA method, and the coordinate value of
one alignment mark (e.g., 29 (n, 1)) of each sample shot is
measured. And, based on the measurement result, values of six error
parameters are determined. Then, arrangement coordinate values upon
calculation of the shot areas are obtained from the transformation
(17) and each shot area is aligned for exposure based on the
obtained arrangement coordinate values.
[0196] Thus, according to the fourth embodiment, the number of
sample shots and that of alignment marks to be measured are large
in several initial wafers while those in the left wafers are the
same as in the conventional EGA method. Therefore, without lowering
the throughput of the whole exposure process so much, it is
possible to improve alignment accuracy by correcting chip rotation,
etc. The methods of the third and fourth embodiments in which the
number of alignment marks is gradually increasing or decreasing can
be applied to the conventional EGA method.
[0197] As in the above embodiments, the method wherein the shot
arrangement error in the wafer is assumed to be linear belongs to
the EGA method. In the EGA method of the above embodiments, the
chip rotation and chip magnification errors are calculated on the
assumption that the chip rotation and chip magnification
(distortion) errors in each shot area is uniform in the same wafer.
Therefore, if the partial arrangement error on the wafer or the
variation (nonlinear condition) of the distortion elements is
large, it is difficult to improve the alignment accuracy.
Consequently, it is desirable to provide an alignment method
wherein the chip rotation and magnification errors can be
preferably corrected and even a wafer having unlinear distortion
can be aligned with high precision. Hereinafter, it will be
described an embodiment of an improved EGA method by which highly
accurate alignment is possible. This alignment method is formed by
applying U.S. patent application Ser. No. 5,146 (filed on Jan. 15,
1993) to the above embodiments.
[0198] Such a fifth preferred embodiment will be described with
reference to FIG. 10. Although the projection exposure apparatus 2
is utilized in this embodiment also, alignment is performed by a
first weighed enhanced global alignment method (hereinafter called
"W1-EGA Method") which is formed by improving the EGA methods in
the first and second embodiments. The alignment by the W1-EGA
method is effective in a wafer with regular nonlinear distortion
and it takes much consideration into a fact that even the wafer
with regular unlinear distortion has partial areas where the
arrangement errors are approximately equal. Then, in the alignment
by the W1-EGA method, weights are given in accordance with
distances between a shot area and sample shots.
[0199] FIG. 10 illustrates a wafer 8 to be exposed in this
embodiment. When determining the coordinate position of the i-th
shot area ESi on the wafer 8 upon calculation, in accordance with
distances LK1 to LK9 between a shot area ESi and m (m=9 in FIG. 10)
sample shots SA1 to SA9, a weight W.sub.in is given to each of
measured coordinate positions (alignment data) of alignment marks
in the nine sample shots. Concretely, the weight W.sub.il is given
to each of measured coordinate positions of two alignment marks
MA1, MB1 in accordance with the distance LK1. Strictly speaking, it
is preferable to give weights in accordance with a distance between
a reference point of the shot area ESi and each alignment mark in
sample shots. Also, it does not necessarily need to measure the
coordinate values of two alignment marks in each shot area.
[0200] Instead of the simple residual error element of the sum of
squared values in the EGA method, a residual error element Ei
obtained by the following equation (18) is defined in the W1-EGA
method. In the equation (18), the coordinate value (FM.sub.NXn,
FM.sub.NYn) is the actually measured coordinate value of an n-th
alignment mark in an n-th sample shot and the coordinate value
(F.sub.NXn, F.sub.NYn) is the coordinate value upon calculation
thereof. 15 Ei = n = 1 m W in [ N = 1 4 { ( F Nxn - F M NXn ) 2 + (
F NYn - F M NY n ) 2 } ] ( 18 )
[0201] Then, ten error parameters (.THETA., W, .GAMMA.x, .GAMMA.y,
O.sub.X, O.sub.Y, .theta., w, rx, ry) satisfying the equation (10)
or the equation (17) is obtained such that the residual error
element Ei is minimized. The sample shots SA1 to SA9 used for each
shot area ESi are the same here, but the distance between the shot
area ESi and the sample shot SAn is different for each shot area
ESi. Accordingly, the weight W.sub.in to be given to the the
coordinate position (alignment data) of the sample shot SAn is
changed for each shot area ESi. The error parameters (.THETA., W,
Rx, Ry, O.sub.X, O.sub.Y, .theta., w, rx, ry) are determined for
each shot area ESi. Then, the wafer rotations .THETA. in the
transformation matrix A in the equation (10) or the equation (17)
and the chip rotation .theta. in the transformation matrix B are
corrected and then the chip magnification error (chip scalings rx,
ry) in the transformation matrix B in the equation (10) or the
equation (17) is corrected.
[0202] Thereafter, the transformation matrices A and O including
the error parameters (.THETA., W, .GAMMA.x, .GAMMA.y, O.sub.X,
O.sub.Y) are used and the arrangement coordinate value upon design
of each shot area ESi on the wafer is substituted for the equation
(12) to obtain the arrangement coordinate value upon calculation of
the reference point of each shot area ESi on the stage coordinate
system (X, Y).
[0203] As disclosed above, when the wafer is rotated, the
arrangement coordinate value is calculated by the conventional EGA
calculation based on the remeasured coordinate values of the
alignment marks.
[0204] Thus, in the W1-EGA method, the weight W.sub.in for the
coordinate data of each sample shot SAn is changed for each shot
area ESi. For example, the weight W.sub.in is expressed by a
function of the distance LKn between the i-th shot area ESi and the
n-th sample shot SAn, as follows. A parameter S is for changing the
degree of weighting. 16 W in = 1 2 S exp { - LKn 2 / ( 2 S ) ] ( 19
)
[0205] As is apparent in the equation (19), the shorter the
distance LKn between the i-th shot area and the sample shot SAn
becomes, the larger the weight W.sub.in given to the alignment data
in the sample shot area SAn becomes.
[0206] Also, when the value of the parameter S is sufficiently
large in the equation (19), the result of the statistics
calculation operation is approximately equivalent to the result of
the calculation by the EGA method in the above embodiments. On the
other hand when the shot area ESi to be exposed is deemed to be the
sample shot SAn and the value of the parameter S is made to
approach to zero, the result of the statistics calculation
operation is approximately equivalent to the result of the
calculation by the die-by-die method wherein the position of a
wafer mark is measured for each shot area for alignment. That is,
in the W1-ECA method, by setting the parameter S to be a proper
value, it is possible to obtain the mean effect between the EGA
method and the die-by-die method. For example, when the value of
the parameter S is set to be small for a wafer having a larger
unlinear element, approximately the same effect (alignment
accuracy) as the die-by-die can be obtained and it is possible to
eliminate the alignment error caused by the unlinear element
preferably. Besides, when the measurement reproducibility of the
alignment is not good, the value of the parameter is set to be
large, whereby approximately the same effect as the EGA method can
be obtained and it is possible to reduce the alignment error by the
mean effect.
[0207] Further, the weighted functional equation (19) may be
provided separately for the X-coordinate values of the alignment
marks and the Y-coordinate values of the alignment marks and the
weight W.sub.in may be set independently for the X-coordinate
values and the Y-coordinate values. In this case, eventhough the
degree (largeness) of the unlinear distortion of the wafer, the
regularity, the step pitch, and the distance of the centers of two
adjacent shot areas (approximately corresponding to the shot size
though it depends on the width of the street line) are different
between in the X and Y directions, it is possible to correct the
shot arrangement error on the wafer with high accuracy by setting
the values of the parameters S independently. At this time, the
value of the parameter S may be differenciated between in the X and
Y directions, as above. Furthermore, although the value of the
parameter S is the same or different between the X and Y
directions, the value of the parameter should be changed properly
in accordance with the largeness of the regular unlinear
distortion, the regularity, the step pitch, the measurement
reproductivity or the like.
[0208] Thus, by changing the value of the parameter S, the effect
can be changed in a range from the EGA method to the die-by-die
method. Accordingly, alignment can be performed with optimum
conditions for each layer and each element (X direction and Y
direction) by changing the alignment flexibly in accordance with,
e.g., the characteristics (e.g., largeness, regularity or the like)
of the nonlinear element, the step pitch, the measurement
reproductivity of the alignment sensor.
[0209] Next, a second weighted enhanced global alignment method
(hereinafter called "W2-EGA method") will be described. To describe
briefly, it is deemed that the wafer is distorted regularly, in
particular, point-symmetrically and the center of the point
symmetry coincides with the center of the wafer (wafer center).
[0210] FIG. 11 illustrates the wafer 8 to be exposed. In the FIG.
11, it is assumed that the distortion center of the wafer 8 (the
center of the point symmetry of the nonlinear distortion), i.e.,
the wafer center is the wafer center Wc, the distance (radius)
between the wafer center Wc and the i-th shot area ESi is the
distance LEi and the distances between the wafer center Wc and m
(m=9 in FIG. 11) sample shots SA1 to SA9 are the distances LW1 to
LW9. In the W2-EGA method similarly to the W1-EGA, method, the
weight W.sub.in is given to measured coordinate positions
(alignment data) of alignment marks of nine sample shots SA1 to SA9
in accordance with the distance LEi and the distances LW1 to LW9.
In the W2-EGA method, two alignment marks (MAi, MBi) are detected
for each sample shot. Thereafter, the residual error element Ei' is
defined in the following equation (20) similarly to the equation
(18) and the error parameters (.THETA., W, .GAMMA.x, .GAMMA.y,
O.sub.X, O.sub.Y, .theta., w, rx, ry) in the equation (10) or the
equation (17) are determined such that the equation (20) is
minimized. 17 Ei ' = n = 1 m W in ' [ N = 1 4 { ( F NXn - F M NXn )
2 + ( F NYn - F M NYn ) 2 } ] ( 20 )
[0211] In the W2-EGA method similarly to the W1-EGA method, the
weight W.sub.in' given to the alignment data is changed for each
shot area ESi, so that the error parameters (.THETA., W, .GAMMA.x,
.GAMMA.y, O.sub.X, O.sub.Y, .theta., w, rx, ry) are determined for
each shot area ESi to determine the chip rotation, the chip
rectangular degree, the chip magnification error and the
arrangement coordinate values upon calculation.
[0212] In order to change the weight W.sub.in' to each sample shot
for each shot area ESi on the wafer 8, the weight W.sub.in' in the
equation (20) is expressed by the function of the distance (radius)
LEi between the i-th shot area ESi and the wafer center Wc. The
parameter S is for changing the degree of weighting. 18 W in ' = 1
2 S exp { - ( LEi - LWn ) 2 / ( 2 S ) } ( 21 )
[0213] As apparent from the equation (21), the nearer the distance
between the sample shot SAn and the wafer center Wc with respect to
the distance between the wafer center Wc and the i-th shot area ESi
becomes, the larger the weight W.sub.in' given to the alignment
data of each sample shot becomes. Namely, the largest weight
W.sub.in' is given to the alignment data of the sample shots
positioned on the circle drawn by the radius LEi from the wafer
center Wc. And, the farther the sample shot SAn is positioned in
the radius direction away from the circle, the smaller the weight
W.sub.in' given to the alignment data of the sample shot SAn
becomes.
[0214] Also, similarly to the W1-EGA method, the value of the
parameter S may be determined properly in accordance with the
required alignment accuracy, the characteristics of the unlinear
distortion (e.g., largeness, regularity or the like), the step
pitch, the measurement reproductivity of the alignment sensor. That
is, when the nonlinear element is comparatively large, the value of
the parameter S is set to be small, whereby the influence of the
sample shots whose distance LWn from the wafer center Wc is larger
can be reduced. On the other hand, when the nonlinear element is
comparatively small, the value of the parameter S is set to be
large, whereby the degradation of the alignment accuracy of the
alignment sensor (or layer) with bad measurement
reproductivity.
[0215] Further, in the W2-EGA method, naturally, the identical
weight W.sub.in' is given to the alignment data of a plurality of
sample shots positioned approximately at the same distance from the
center of the point symmetry on the wafer, i.e., the plurality of
shot areas positioned on the same circle having the center of the
point symmetry. Therefore, when a plurality of shot areas are
positioned on the circle having the center of the point symmetry
the weighting and the statistic calculation are performed only in
one of those shot areas so as to obtain the error parameters
(.THETA., W, .GAMMA.x, .GAMMA.y, O.sub.X, O.sub.Y, .theta., w, rx,
ry) and the calculated error parameters can be used for the
remaining shot areas to determine the chip rotation, the chip
rectangular degree, the chip magnification error and the coordinate
positions. As a result, the calculation amount can be reduced.
[0216] In order to realize the preferable alignment of sample shots
in the W2-EGA method, it is desirable to specify the sample shots
so as to be symmetrical with respect to the center of the point
symmetry of the unlinear distortion, i.e., the wafer center Wc and,
e.g., to specify the sample shots in the X-shape or the cross shape
on the basis of the wafer center Wc. Besides, the same arrangement
in the W1-EGA method may be preferable. When the center of the
point symmetry of the unlinear distortion is not the wafer center
Wc, the arrangement of the sample shots may be in the X shape or
the cross shape on the basis of the center of the point symmetry.
Also, when determining the values of the error parameters, the
weighted function in the equation (21) may be provided
independently for the X and Y directions. Besides, it is needless
to say that the weighted function may be provided for each
alignment mark.
[0217] In the W1-EGA method and the W2-EGA method, when correcting
the rotation error and the magnification error based on the four
error parameters (0, w, rx, ry), the corrections may be performed
for each shot area by using the parameters obtained for each shot
area. Also, a set of parameters obtained for each shot area may be
averaged to obtain a set of parameters based on which the
corrections may be performed at a time for the whole of the wafer.
Further, the wafer may be divided into a plurality of blocks and
the corrections may be performed for each block. Furthermore,
according to the W2-EGA method, in the shot areas positioned on the
concentric circle with respect to the center of the point symmetry,
there is no need to obtain the parameters for each shot area and
the parameters may be obtained for one of those shot areas.
[0218] Next, referring to FIGS. 15 to 17, explanation will be made
of a sixth embodiment of the present invention. In this embodiment,
the positional alignment (or superposition) between the pattern
image of the reticle 2 and the chip pattern on the wafer 8 is to be
carried out even in consideration with an error in the rotation of
the reticle 2 and/or an error in the magnification of the
projection optical system 7. It is noted that the explanation will
be made on the premise that the use of the projection and exposure
device shown in FIG. 2 is also used in this embodiment.
[0219] Referring to FIG. 16A which shows the structure of the
reticle 2 used in this embodiment, an exposure circuit pattern 141
is formed in the center part of the reticle 2, and eight identical
alignment marks 143A to 143H are also formed in the image field
142R of the projection optical system 7 around the circuit pattern
141. The positions of the alignment marks 143A to 143H are
beforehand determined in the rectangular coordinate system (.xi.R,
.eta.R) having its original point (0, 0) located at the center of
the reticle 2. In addition to the alignment marks 143A to 143H,
alignment marks for positioning the reticle 2 on the reticle stage
3 are formed on the reticle 2 although they are not shown.
[0220] Referring to FIG. 16B which shows the shape of the alignment
mark 143A, the alignment mark 143A is the one in which a line and
space pattern 145 composed of a plurality of opening patterns laid
in the direction .xi.R and a line and space pattern 146 composed of
a plurality of opening patterns laid in the direction .eta.R, are
formed in a shading film 144. With the use of these line and space
patterns 145, 146, the positions of the alignment mark 143A in the
directions .xi.R, .eta.R are designated. It is noted that the other
alignment marks 143B to 143H also has the same shape as that of the
alignment mark 143A. Further, patterns conjugate with the line and
space patterns 145, 146 shown in FIG. 16B are formed in the slit
plate of the photoelectric sensor PS shown in FIG. 2.
[0221] Next, explanation will be made of exposure operation of this
embodiment with reference to the flow-chart shown in FIG. 15. After
the reticle 2 is loaded on the reticle stage 3 at step 301, at step
302, the reticle 2 is aligned. That is, with the use of an
alignment microscope (which is not shown), as disclosed in U.S.
Pat. No. 4,710,029, the alignment marks on the reticle 2 (which are
different from the alignment marks 143A to 143H shown in FIG. 16B),
are detected so as to position the reticle 2 in order to align the
center of the reticle 2 with the optical axis 7a of the projection
optical system 7.
[0222] Thereafter, at step 303, the coordinate positions of the
projected images of more than three of the eight alignment marks
143A to 143H in the stage coordinate system (X, Y) are
measured.
[0223] Referring to FIG. 17 which shows the images of the alignment
marks 143A to 143H projected onto the wafer stage 10 from the
reticle 2, the images 143AW to 143HW of the eight alignment marks
are projected in the exposure field 142 of the projection optical
system 7. Further, the image of the coordinate system (.xi.R,
.xi.R) projected onto the wafer stage 10 from the reticle 2 in an
ideal image forming condition the projection optical system 7 is
shown by the coordinate system (.xi., .eta.). In this embodiment,
designed arrangement coordinates (CR.xi..sub.Xn, CR.eta..sub.Yn,
n=1 to 8) of the alignment marks 143A, 143H in the coordinate
system (.xi.R, .eta.R) on the reticle 2 are converted into
arrangement coordinates (CR.sub.Xn, CR.sub.Yn) of the alignment
mark images 143AW to 143HW in the coordinate system (.xi., .eta.)
on the wafer stage 10. Further, the arrangement coordinates of the
alignment mark images 143A to 143H are denoted by (FR.sub.Xn,
FR.sub.Yn).
[0224] In this case, since the reticle 2 has the following error
factors with respect to the stage coordinate system.(X, Y), the
arrangement coordinates (CR.sub.Xn, CR.sub.Yn) do not coincide with
the arrangement coordinates (FR.sub.Xn, FR.sub.Yn)
[0225] (1) The rotation of the reticle 2:
[0226] This causes an Error .THETA..sub.R in residual rotation of
the reticle converted into the wafer side, in the coordinate system
(.xi., .eta.), with respect to the stage coordinate system (X,
Y);
[0227] (2) The orthogonal degree of the reticle coordinate system
(.xi., .eta.):
[0228] This causes an orthogonal degree error WR since the patterns
in the .xi.-axis and the .eta.-axis are not precisely orthogonal to
each other due to errors in depiction:
[0229] (3) Errors in magnification of in the directions .xi., .eta.
in the reticle coordinate system (.xi., .eta.):
[0230] These are caused by an error in the length of a pattern on
the reticle 2, or caused by a deviation (for example 1/5) of the
projection magnification of the projection optical system 7 from
its designed value. These errors are denoted by magnification
errors RRx, RRy, respectively in the directions .xi., .eta.. It is
noted that the magnification error RRx in the direction .xi. is
exhibited by the ratio between measured and designed values of the
distance between two alignment marks on the wafer stage in the
direction .xi., and the magnification error RRy in the direction
.eta. is exhibited by the ratio between measured and designed
values of the distance between two alignment marks on the wafer
stage in the direction .eta..
[0231] (4) Offset of the reticle coordinate system (.xi., .eta.)
with respect to the stage coordinate system (X, Y):
[0232] This is caused by such a fact that the projected image of
the reticle 2 is slightly deviated with respect to the wafer stage
10 as a whole, and is denoted by offset errors OR.sub.x,
OR.sub.y.
[0233] In the case of the above-mentioned error factors (1) to (4)
being concerned, the coordinate value (FR.sub.Xn, FR.sub.Yn) on the
stage coordinate system (X, Y) of the alignment mark image having
the designed coordinate value (CR.sub.Xn, CR.sub.Yn) can be
expressed as follows: 19 ( FR Xn FR Yn ) = ( RRx 0 0 RRy ) ( cos R
- sin R sin R cos R ) ( 1 - tan W R 0 1 ) ( CR Xn CR Yn ) + ( O R X
OR Y ) ( 22 )
[0234] Estimating that the orthogonal degree error W.sub.R and the
residual rotation error .THETA..sub.R are very small, equation (22)
is subjected to a first order approximation is carried out so as to
obtain: 20 ( FR Xn FR Yn ) = ( RRx - RRx ( WR R + R ) RRy R RRy ) (
CR X CR Yn ) + ( O R x O R y ) ( 23 )
[0235] Next, matrices and vectors are substituted with matrices
FRn, ARn and vectors CRn, OR as follows: 21 FRn = ( FR Xn FR Yn ) ,
AR = ( RRx - RRx ( W R + R ) RRy R RRy ) CRn = ( CR Xn CR Yn ) , 0
R = ( OR x OR y ) ( 24 )
[0236] Accordingly, equation (23) is exhibited as follows:
FRn=AR.multidot.CRn+OR (25)
[0237] The purpose of the this embodiment is to obtain four errors
RRx, RRy, W.sub.R, .THETA..sub.R (which will be sometimes denoted
as "error parameters") in the matrix AR in the equation (25), and
two offset errors OR.sub.x, OR.sub.y in the vector OR. For example,
an EGA type calculating technique as disclosed in U.S. Pat. No.
4,780,617 or U.S. Pat. No. 4,833,621 can be used for this purpose.
That is, since the number of error parameters is six, the
coordinate positions of more than three of the alignment mark
images 143AW to 143HW in the stage coordinate-system (X, Y) are
measured, and the values of the six error parameters are obtained
in such a way that the sum of squares of the measured coordinate
positions and calculated coordinate positions given by equation
(25) are minimized by these six parameters.
[0238] It is noted that each of the alignment marks 143AW to 143HW
is a two-dimensional mark in combination two one-dimensional marks,
and accordingly, although more than three of the alignment marks
are used in this embodiment, the positions of more than six
alignment marks have to be measured if only one-dimensional marks
are selected. Further, such a condition that more than three
alignment mark images selected from a group consisting of the
alignment mark images 143AW to 143HW shown in FIG. 17 are not on
one and the same line is required. Further, it is desirable that
the alignment mark images from which coordinate positions are
measured are uniformly distributed without deviation. For example,
they are preferably distributed with point symmetry with respect to
the optical axis 7.
[0239] Accordingly, at step 303, the coordinate positions, in the
stage coordinate system (X, Y), of four alignment mark images
143BW, 143DW, 143FW, 143HW which are substantially point-symmetric
with respect to the optical axis 7a, as shown by oblique lines, are
measured. In this case, an X-Y plane is scanned with the
photoelectric sensor PS shown in FIG. 2 so as to obtain a position
where a photoelectrically converted signal which is obtained from
the photoelectric sensor PS at every alignment mark becomes
maximal. Thereafter, at step 304, completely similar to the
conventional EGA type technique, the least square method is used
for obtaining values of the six parameters (RRx, RRy, W.sub.R,
.THETA..sub.R, OR.sub.x, OR.sub.y) which satisfy equation (25).
[0240] It is noted that although the six parameters are calculated
with the use of the EGA type calculation technique in this
embodiment, the above-mentioned W1-EGA type or W2-EGA type
calculation technique can be applied for calculating the six error
parameters. In this case, each of measured data (coordinate
positions) of a plurality of alignment mark images shown in FIG. 17
is weighed in accordance with, for example, a distance from the
center of the reticle 2 to an alignment mark, and thereafter, the
six parameters which satisfy equation (18) or (20) are obtained
with the use of a least square method.
[0241] Further, in a certain case, the orthogonal degree error WR
is neglected (regarded as zero), and the magnification errors RRx,
RRy can be sometimes commonly substituted by an averaged value RR
(=(RRx+RRy)/2). In this case, the matrix AR in equation (25) can be
approximated as follows: 22 AR RR ( 1 - R R 1 ) ( 26 )
[0242] In this equation (26), since the number of error parameters
is reduced to four, the number of alignment mark images to be
measured for the application of the least square method can be more
than two in the case of the two-dimensional marks.
[0243] Next, at step 305, the wafer 8 shown in FIG. 4A is loaded on
the wafer holder 9. Chip patterns have been already formed in the
shot areas on the wafer 8, respectively, during the previous
process step. Then, at step 306, an original point is set for the
wafer 8 (prealignment), and further at step 307, with the use of
the off-axis type alignment system 15, the coordinate values
(FM.sub.NXn, FM.sub.NYn), in the stage coordinate system (X, Y), of
more than five alignment marks (29-n, 30-n, 34-n, or 35-n) on the
wafer 8 are measured. In this embodiment, although the actually
measured alignment marks are required to be selected from more than
three shot areas 27-n, it is not always necessary to select four
alignment marks from one shot area, but it is sufficient to select
at least one alignment mark for each of the shot areas.
[0244] It is noted that the designed arrangement coordinate values
(C.sub.Xn, C.sub.Yn), in the coordinate system (.alpha., .beta.) on
the wafer 8, of the reference points 28-n in the plurality of shot
areas 27-n selected on the wafer, and the designed coordinate
values (relative coordinate values) (S.sub.NXn, S.sub.NYn), in the
coordinate system (x, y) on the shot-areas 27-n, of the alignment
marks have been previously known. Accordingly, completely similar
to the first embodiment, at step 308, by substituting the designed
arrangement coordinate values (C.sub.Xn, C.sub.Yn) on the reference
points in the shot areas to which the measured alignment marks
belong, and the designed relative coordinate values (S.sub.NXn,
S.sub.NYn) relating to the reference points of the alignment marks
into the right side of equation (15), calculated coordinate values
(F.sub.NXn, F.sub.NYn) with which the alignment marks should be on
the stage coordinate system (X, Y) are obtained.
[0245] Further, ten error parameters (.THETA., W, .GAMMA.x,
.GAMMA.y, O.sub.X, O.sub.Y, .theta., w, .gamma.x, .gamma.y) which
satisfy equation (17) are obtained by a least square method.
Specifically, differences (E.sub.NXn, E.sub.NYn) between the
measured coordinate values (FM.sub.NXn, FM.sub.NYn) and the
calculated coordinate values (F.sub.NXn, F.sub.NYn) thereof are
regarded as alignment errors. Further, the sums of squares of five
groups, that is, more than 10 alignment errors (E.sub.NXn,
E.sub.NYn) are partially differentiated by ten error parameters,
respectively, and the equations are established so that each of
their values becomes zero. Further, ten established simultaneous
equations are solved in order to obtain ten error parameters.
[0246] Next, at step 309, with the use of the rotation error
.THETA..sub.R of the reticle in the transforming matrix AR in
equation (25) as a reference value, the sum (.THETA.+.theta.) where
.THETA. is a wafer rotation in the transforming matrix A in
equation (16), and .theta. is a chip rotation in the transforming
matrix B in equation (16) is adjusted to the rotation error
.THETA..sub.R. Therefor, the wafer 8 is rotated by the wafer stage
10 while the running direction of the wafer stage 10 is set to be
oblique so as to be adjusted to the rotation of the reticle 2. It
is noted that the reticle 2 can be rotated, instead of the rotation
of the wafer 8.
[0247] However, if the wafer 8 is rotated, since offset errors
(O.sub.x, O.sub.Y) of the wafer 8 vary, after the coordinate values
of the alignment marks are measured again, the error parameters
have to be again obtained with the use of the conventional EGA
computation. Accordingly, for example, in the case of the rotation
of the wafer 8 by a predetermined angle, the coordinate positions,
in the stage coordinate system (X, Y), of alignment marks in at
least three shot areas on the wafer 8 are measured. Further, from
the result thereof, six error parameters (.THETA., W, Rx, Ry,
O.sub.x, O.sub.Y) are obtained, and shot areas are positioned in
accordance with arrangement coordinates calculated from these six
error parameters, thereby the exposure is carried out. This can be
also used for confirming whether a new residual rotation error
.THETA. after the rotation of the wafer 8 has a value which
corresponds to the rotated angle at step 309 or not.
[0248] Further, the orthogonal degree error W.sub.R of the reticle
2 and the orthogonal degree error w of the chip can not be strictly
compensated for, but these errors can be restrained to be small by
rotating the wafer 8. Further, the degree of rotation of the
reticle 2 can be optimized so as to minimize the sum of the
absolute values of the rotation error .THETA. of the wafer 8, the
rotation error .theta. of the chip and the orthogonal degree error
w.
[0249] Next, at step 310, the projection magnification of the
projection optical system 7 is adjusted through the intermediary of
the image-forming characteristic control device 14 so that
magnification errors RRx, RRy of the projected image of the reticle
2 in the transforming matrix AR in equation (25), and the chip
scaling errors rx, ry in the transforming matrix B in equation (16)
are compensated for. For this purpose, if a pattern on the first
layer is exposed onto the wafer 8, the projection magnification can
be adjusted so that the magnification errors RRx, RRy are precisely
adjusted to zero. In a condition in which the magnification errors
RRx, RRy become precisely zero, the projected image of the pattern
of the reticle 2 by the projection optical system 7, has a size
equal to a designed value. Meanwhile, if pattern images of the
reticle 2 on layers subsequent to the second layer are exposed, the
projection magnification of the projection optical system 7 is
compensated with the use of the chip scaling errors rx, ry as
references. Accordingly, the size of the projected image of the
reticle 2 becomes equal to that of a chip pattern which has been
already formed on the wafer 2.
[0250] It is noted that as shown in FIG. 17, since the alignment
mark image 143AW to 143HW of the reticle 2 in this embodiment are
sometimes formed outside of a rectangular exposure area within the
exposure field 142 of the projection optical system 7, the
measurement of the magnification of the projection optical system 7
is greatly affected by distortion. Accordingly, with the use of a
reference reticle with which alignment mark images have been
previously projected within the exposure area, the offset
compensation for the projection magnification of the projection
optical system 7 can be made so as to allow the magnification of
the projected image of this reference reticle to be equal to the
designed value. In this case, the compensation of the projection
magnification of the projection optical system 7 during the
exposure of the pattern on the first layer, is not necessary.
[0251] Thereafter, at step 311, with the use of the transforming
matrices A and O including elements composed of error parameters
obtained at step 308, by substituting the designed arrangement
coordinate values (C.sub.Xn, C.sub.Yn) of the reference points 28-n
of the respective shot areas 27-n on the wafer 8 into equation
(12), the calculated arrangement coordinate values (G.sub.Xn,
G.sub.Yn) of the reference points 28-n in the stage coordinate
system (X, Y) are obtained. However, if the wafer 8 is rotated in
order to compensate the rotation error at step 305, the calculated
arrangement coordinate values (G.sub.Xn, G.sub.Yn) of the reference
points 28-n in the stage coordinate system (X, Y) are obtained from
the coordinate values of the remeasured alignment marks.
[0252] Further, at step 312, with the use of the thus calculated
arrangement coordinate values (G.sub.Xn, G.sub.Yn) and a previously
obtained base line value, the reference points 28-n of the shot
areas 27-n on the wafer 8 are positionally aligned successively
with predetermined positions in the exposure field of the
projection optical system 7, and then, the pattern image of the
reticle 2 is transferred onto the shot areas 27-n. Further, after
the exposure for all shot areas on the wafer 8 is completed, the
development and the like are carried out for the wafer 8.
[0253] In this embodiment, as shown in equations (25) and (17),
since not only the transforming matrices A and O but also the
parameters such as the rotation error of the reticle, the
magnification error of the reticle, the chip rotation and the chip
scaling error, and the like are taken into consideration, the
affection by the rotation error of the reticle 2, the magnification
error of the projection optical system 7, the expansion and
contraction, and the rotation of the chip patterns themselves, can
be restrained to be small, and further, the projected images of
chip patterns and the reticle pattern in the shot areas on the
wafer can be superposed with each other over their entire
surfaces.
[0254] It is noted that although multi-point measurement is carried
out in the respective shot areas on the wafer 8 in this embodiment,
the position of a specific one mark in each of the shot areas can
be detected by directly applying the usual EGA type technique. In
this case, the transforming matrix B in equation (17) is neglected,
and further, for example the wafer rotation .THETA. is adjusted to
the rotational error .THETA..sub.R of the reticle.
[0255] Further, in this embodiment, no positive compensation for
the orthogonal degree error of the reticle 2 is carried out.
However, for example, a part of lenses constituting the projection
optical system 7, have toroidal surfaces, and further, a mechanism
for rotating the lenses around the optical axis, is provided, with
which the lenses can be rotated so as to minimize the orthogonal
degree error W.sub.R of the projection image. With this
arrangement, the orthogonal degree error W.sub.R caused by a
depiction error or the like of the reticle 2 can be made to be
small.
[0256] Further, in this embodiment, during compensation of the
reticle rotation, or during compensation of the magnification of
the projected image of the reticle (compensation with pattern
exposure subsequent to the second layer), the rotation, and the
expansion and contraction of the wafer and the chip are taken into
consideration. However, if it is found that the magnification
error, the rotation errors and the like is very small, from printed
conditions of wafers in one and the same rot, to which the exposure
process has been completed, and so forth, the compensation of the
rotation of the reticle or the compensation of the projection
magnification of the projection optical system 7 can be made only
by use of the result of the measurement (EGA measurement) based
upon equation (25).
[0257] Further, although the alignment system (equations (17) or
(10)) as explained in the first embodiment, is used from steps 303
to 311, any of the EGA type technique as disclosed in the U.S. Pat.
No. 4,780,617, the W1-EGA type technique or W2-type EGA technique
which have been explained in the fifth embodiment, can be also
used.
[0258] Further, although the coordinate positions, in the stage
coordinate system (X, Y), of the alignment marks on the reticle are
measured with the use of the photoelectric sensor PS (refer to FIG.
2) disclosed in the U.S. Pat. No. 4,629,313 at step 305 in FIG. 15
the coordinate positions of the alignment marks on the reticle can
be measured with the use of the system disclosed, for example, in
U.S. Pat. No. 4,780,616.
[0259] In addition to the step and repeat type exposure apparatus
(e.g., the reduction projecting type stepper, isometric
magnification projection type stepper), the present invention is
applicable to the step and scan type exposure apparatus or the
proximity type stepper (X-ray exposure apparatus or the like).
Furthermore, the present invention is applicable to an inspecting
apparatus (defect inspector, prober or the like) for inspecting a
semiconductor wafer or a reticle with a plurality of chip patterns,
wherein alignment is performed by the step and repeat method for
each chip with respect to the reference position such as the
inspection visual field, the probe needle or the like.
[0260] When applying the above alignment method to the scan type
exposure apparatus such as the step and scan type exposure
apparatus, a wafer is positioned to a position determined by adding
a predetermined offset (the value to be determined unconditionally
in accordance with the pattern size, the approach run area of the
reticle and the wafer, or the like) to the coordinate position
obtained in the above embodiments and thereafter the scan exposure
is effected.
[0261] Next, a seventh embodiment of the present invention will be
described with reference to FIGS. 18 to 24.
[0262] FIG. 19 illustrates an essential portion of a projection
exposure apparatus which is provided with an alignment device to be
used in the seventh embodiment. Referring to FIG. 19, an
illumination light for exposure (g-ray and i-ray of a mercury-ark
lamp or ultraviolet pulse ray from an excimer laser source) IL
irradiates a pattern area PA of a reticle R with a uniform
distribution of illuminance intensity through a condenser lens CL.
The illumination light IL passing through the pattern area PA
enters a projection optical system PL which is telecentric on both
sides (or one side) reaches a wafer W. The projection optical
system PL is compensated to have an optimal aberration with respect
to a wavelength of the illumination light IL, and the reticle R and
the wafer W are conjugate with each other under the compensated
wavelength. Description will now be made on a case where the Z axis
is taken in parallel to the optical axis AX of the projection
optical system PL, the X axis is taken in parallel to the sheet
surface of FIG. 19 on a plane perpendicular to the Z axis, and the
Y axis is taken in parallel to the sheet surface of the FIG.
19.
[0263] Now, the reticle R is supported by a reticle stage RS which
is finely movable two-dimensionally, and the reticle R is
positioned with respect to the optical axis AX of the projection
optical system PL by detecting a reticle alignment mark formed in
the circumference of the reticle R by the use of a reticle
alignment system which comprises a mirror 416, an objective lens
417, and a mark detection system 418. On the other hand, the wafer
W is mounted on a wafer stage ST which is two-dimensionally moved
by a driving system 413, and a coordinate value of the wafer stage
ST is successively measured by an interferometer 412. A stage
controller 414 controls the driving system 413 on the basis of the
measured coordinate value and the like from the interferometer 412
so as to control a movement or positioning of the wafer stage ST. A
reference mark FM which is used for base line measurement or the
like is provided on the wafer stage ST. The baseline measurement is
to measure a distance (base line) between the center of detection
of an alignment sensor and the center of the exposure field of the
projection optical system PL. In this embodiment, this base line is
obtained in advance.
[0264] Next, description will be made on a wafer mark serving as an
alignment mark which is attached in each shot area on the wafer
W.
[0265] FIG. 20A shows a positional relationship between one shot
area 27-n on the wafer W and pairs of wafer marks 29 (n, 1) to 29
(n, 4) attached in said shot area 27-n. In this FIG. 20A, the four
sides of the shot area 27-n are surrounded by a scribe line SCL.
Then, four measuring points SC1 to SC4 are set at the apexes of a
substantially square form of the shot area 27-n, and the pairs of
wafer marks 29 (n, 1) to 29 (n, 4) are respectively formed in the
vicinity of the measuring points SC1 to SC4. In this embodiment,
the pair of wafer marks 29 (n, 1) in the vicinity of the measuring
point SC1 is comprised of a wafer mark MX1 arranged at a
predetermined pitch in the X direction and a wafer mark MY1
arranged at a predetermined pitch in the Y direction. In the same
manner, the pairs of wafer marks 29 (n, 2) to 29 (n, 4) are
comprised of wafer marks MX2 to MX4 for the X axis and wafer marks
MY2 to MY4 for the Y axis. The wafer marks MX1 to MX4 have the same
configuration, while the wafer marks MY1 to MY4 have also the same
configuration.
[0266] The reference mark 28-n at the center of the shot area 27-n
is on the optical axis AX of the projection optical system PL in
the exposure mode. Then the centers of, for example, the wafer
marks MX1 and MY1 are positioned on straight lines which
respectively pass through the measuring point SC1 and are extending
in the X and Y directions. The wafer mark MX1 is used for detecting
the position of the measuring point SC1 in the X direction, while
the wafer mark MY1 is used for detecting the position of the
measuring point SC1 in the Y direction. Each of the wafer marks MY1
and MX1 is a multi-mark which has a plurality of linear patterns
arranged in parallel. In the same manner, the other pairs of the
wafer marks 29 (n, 2) to 29 (n, 4) are used for detecting the
positions of the measuring points SC2 to SC4, respectively.
[0267] FIG. 20B shows an enlarged view of the wafer mark MX1, as a
representative example, in which five linear patterns P.sub.1,
P.sub.2, P.sub.3, P.sub.4, and P.sub.5 extending in the Y direction
are arranged in the X direction at a substantially constant pitch.
FIG. 20C shows a cross-sectional structure of said wafer mark MX1
in the X direction. In this FIG. 20C, each of five linear patterns
P.sub.1 to P.sub.5 is formed in a convex form projecting from the
ground of the wafer W, and the upper face thereof is coated with a
photoresist layer PR. As also shown in FIG. 20B, a straight line
which passes through the measuring point SC1 in the shot area 27-n
and is in parallel to the Y axis is designed to pass through the
center of the width of the central linear pattern P.sub.3 of the
wafer mark MX1. Note that the wafer mark MY1 has the same
configuration, which is comprised of five linear patterns, and the
center line of the central linear pattern is aligned with the
center line of the measuring point SC1 in the Y direction.
[0268] In the present embodiment, since four pairs of wafer marks
are provided in each shot area 27-n, an alignment by the EGA method
of four points can be performed in the shot area.
[0269] Returning to FIG. 19, in this embodiment, there are provided
an alignment sensor (hereinafter called the "FIA system") 436 of
the FIA method (image pick-up method) of the off-axis system
serving as the first alignment sensor and an alignment sensor
(hereinafter called the "LIA system") 410 of the LIA method (laser
interferometric alignment method) of the TTL system serving as the
second alignment sensor. In this embodiment, the wafer marks MX1 to
MX4 for the X axis shown in FIGS. 20A to 20C are subjected to the
detection by the LIA system 410 for the X axis of the TTL system
and the FIA system 436 of the off-axis system in common, while the
wafer marks MY1 to MY4 for the Y axis are subjected to the
detection by the LIA system (not shown) for the Y axis of the TTL
system and the FIA system 436 of the off-axis system in common.
Note that another wafer mark may be provided to be detected by the
LIA sensor 410 separately from that to be detected by the FIA
system 436. In this case, there occurs no problem if an amount of a
positional deviation between the different kinds of wafer marks has
been obtained in advance.
[0270] Next, a configuration of an alignment sensor will be
described in full. First, in the LIA system 410, a laser beam LB
from the laser source 1 is red monochromatic light such as He--Ne
laser light and is non-photosensitive for the photoresist layer on
the wafer W. This laser beam LB is incident on a heterodyne beam
generation optical system 2 which includes an acoustic optical
modulation element and the like, while two laser beams LB1 and LB2
which have slightly different frequencies and are interferable with
each other are emitted at predetermined cross angles from the
heterodyne generation optical system 2.
[0271] The emitted two laser beams LB1 and LB2 are once
Fourier-transformed via a mirror 403a and a lens system 404, and
then reversely Fourier-transformed via a mirror 403b and the
objective lens 406. Then, the two laser beams are reflected by a
mirror 407 which is arranged slantingly at an angle of inclination
of 450 below the reticle R and enter the circumference of the field
of view of the projection optical system PL. In this case, the
mirror 407 is fixed to be outer than the circumference of the
pattern area PA of the reticle R and within the field of view of
the projection optical system PL. Accordingly, the laser beams LB1
and LB2 crossing on the wafer W are positioned outside a projected
image of the pattern area PA. In order to detect the position of an
alignment mark (wafer mark) in the form of a diffraction grating
attached in each shot area of the wafer W in the X direction by the
use of this crossing pair of laser beams, design is made such that
a pitch of the wafer mark and a cross angle of the two laser beams
have a predetermined relationship so as to emit the diffraction
grating in the same direction from said wafer mark.
[0272] FIG. 22 shows a state in which the two laser beams LB1 and
LD2 are applied symmetrically to the predetermined wafer mark MX1
on the wafer W. In this FIG. 22, a diffracted light LB3 consisting
of +1st-order diffracted light of the laser beam LB1 and -1st-order
diffracted light of the laser beam LB2 are emitted from the wafer
mark MX1 perpendicularly upward. Since the laser beam LB1 and the
laser beam LB2 are interferable with each other and have slightly
different frequencies, the diffracted light LB3 is a heterodyne
beam with a light intensity which changes using said difference in
the frequency as a beat frequency. Also, since the phase of said
diffracted light LB3 is changed in accordance with the position of
said wafer mark MX1 in the X direction, the phase of a beat signal
which is obtained by photoelectrically converting said diffracted
light LB3 is compared with the phase of a beat signal which is
obtained by photoelectrically converting, for example, a reference
heterodyne beam so as to obtain the position of said wafer mark MX1
in the X direction with a extremely high resolution (e.g., in the
order of a several nm).
[0273] Returning to FIG. 19, a diffracted light which is generated
from the wafer mark on the wafer W substantially perpendicularly
upward passes through the projection optical system PL, the mirror
407, the objective lens 406 and the mirror 403b, is reflected by a
small-sized mirror 405 which is arranged between the two laser
beams LB1 and LB2 on the incident side, and reaches a
light-receiving element 408. A beat signal obtained by effecting
photoelectrical conversion in the light-receiving element 408 is
supplied to an LIA calculating unit 409, together with a position
measurement signal PDS of the wafer stage ST from the
interferometer 412. A reference beat signal which is obtained by
photoelectrically converting the reference heterodyne beam
generated in the heterodyne beam generation optical system 402 is
also supplied to the LIA calculating unit 409. The LIA calculating
unit 409 compares the phases of the two beat signals with each
other to obtain the information AP.sub.1 on the position of the
wafer mark to be measured in the X direction, and supplies this
information to a main control system 500.
[0274] In this connection, when, for example, the phase of the
reference beat signal is aligned with the phase of the beat signal
corresponding to the wafer mark, an X-coordinate of, for example,
the wafer stage ST becomes the X-coordinate of the wafer mark as it
is. When the phase of the reference beat signal deviates from that
of the beat signal corresponding to the wafer mark, a coordinate
value which is obtained by adding the X-coordinate of said wafer
stage ST to a value converted from an amount of deviation of said
phase into a displacement becomes an X-coordinate of said wafer
mark. Also, since the phase of the beat signal is changed at, for
example, a pitch cycle which is 1/2 of that of the wafer mark by
360.degree., it is required to position the wafer W in advance at a
precision of, for example, at a pitch which is 1/2 of that the
wafer mark by a search alignment (which is described later).
[0275] In the foregoing description, the laser source 401, the
heterodyne beam generation optical system 402, the mirrors 403a and
403b, the lens system 404, the mirror 405, the objective lens 406,
the mirror 407, the light-receiving element 408, the LIA
calculating unit 409 and the projection optical system PL
constitute the LIA system 410 for the wafer W. Note that this LIA
system 410 is an alignment sensor for detecting the position of a
wafer mark for the X axis, and these is also provided an LIA system
(not shown in the figure) having the same configuration for
detecting the position of the wafer mark in the Y direction for the
Y axis.
[0276] Next, in the FIA system 436 serving as the first alignment
sensor, a light having a wide band range generated from a halogen
lamp 420 is converged onto one end surface of an optical guide 422
by a condenser lens 421. The light, after passing through the
optical guide 422, passes through a filter 423 which cuts off a
photosensitive wavelength (shortwave length) range of the
photoresist layer and an infrared wavelength range, and reaches a
half mirror 425. The illumination light reflected by this half
mirror 425 enters an objective lens 427 after being reflected by a
mirror 426 to be substantially horizontal, and is further reflected
by a prism (mirror) 428 which is fixed in the vicinity of the lower
portion of a lens barrel of the projection optical system PL so as
not to shield the field of view of the projection optical system
PL. The illumination light then irradiates the wafer W
substantially perpendicularly. Though not shown in this figure, an
appropriate illumination field stop is provided at a position
conjugate with the position of the wafer W with respect to the
objective lens 427 in an optical path from the emitting end of the
optical guide 422 to the objective lens 427. The objective lens 427
is made as telecentric. An image of the emitting end of the optical
guide 422 is formed on a surface 427a of an aperture stop (the same
as the pupil) of the objective lens 427 so as to perform Kohler's
illumination. Design is made so that the optical axis of the
objective lens 427 is fixed to be perpendicular on the wafer W, and
no deviation is caused in the mark position due to falling of the
optical axis when the mark is detected.
[0277] The reflected light from the wafer W passes through the
objective lens 428 and the half mirror 425, and is imaged on an
index plate 430 by the lens system 429. This index plate 430 is
provided to be conjugate with the wafer W by the use of the
objective lens 427 and the lens system 429, and is provided with
index marks each in the form of a straight line and projecting in
the X and Y directions, respectively, in a rectangular transparent
window. Accordingly, the image of the wafer mark on the wafer W is
formed in the transparent window of the index plate 430. Light
beams from the wafer mark image and the index marks pass through a
first relay system 431 and enter the half mirror 432. Each of the
light beams is split into two beams by the half mirror 432, so as
to form images on image pick-up elements 434X and 434Y of a CCD
camera, or the like, respectively, through a second relay system
433X and the SSY. Image pick-up signals from the image pick-up
elements 434X and 434Y are supplied to the FIA (field image
alignment) calculating unit 435, together with a position
measurement signal PDS from the interferometer 412. Deviation of
the wafer mark image with respect to the index mark on the index
plate 430 is calculated by the FIA calculating unit 435 on the
basis of the waveforms of the image pick-up signals. In this case,
the position of the wafer mark in the X direction is detected by
processing the image pick-up signal from the image pick-up element
434X for the X axis, while the position of the wafer mark in the Y
direction is detected by processing the image pick-up signal from
the image pick-up element 434Y for the Y axis.
[0278] FIG. 21 shows the wafer mark MX1 detected by the image
pick-up element 434X for the X axis. As shown in FIG. 21, the wafer
mark MX1 to be detected is positioned between the index marks 430a
and 430b on the index plate 430 (see FIG. 19), and the accurate
position XA of the wafer stage ST in the X direction at that time
is calculated. The image pick-up element 434X electrically scans
the five linear patterns P1 to P.sub.5 of the wafer mark MX1 and an
image by the index marks 430a and 430b along a scan line SL. In
this case, when there is only one scan line, for example, it is
disadvantageous in terms of an SN ratio so that levels of image
pick-up signals which can be obtained by a plurality of horizontal
scan lines supplied to a video sampling area VSA indicated by a
broken line may be weighted-averaged for each pixel in the
horizontal direction. Each image pick-up signal has rising and
falling waveform portions on its both sides for each of the index
marks 430a and 430b. The positions XR.sub.1, XR.sub.2 of these
portions (the positions on the pixel) have been obtained in
advance, and the position XR.sub.0 of the median thereof has been
also obtained.
[0279] On the other hand, since the image pick-up element 434X
photoelectrically detects a bright field image of the wafer mark
MX1, a light to return to the objective lens 427 is extremely
decreased by scattering of the light in the right and left step
edges of each of the five linear patterns P.sub.1 to P.sub.5. For
this reason, the right and left edges of each of the linear
patterns P.sub.1 to P.sub.5 are image-picked up as black lines. As
a result, a waveform of the image pick-up signal has its bottom at
a position corresponding to the right edge or the left edge of each
linear pattern.
[0280] The FIA calculating unit 435 calculates the position Xm of
the center (the straight line CX) of the wafer mark MX1 (the
patterns P.sub.1 to P.sub.5) in the X direction on the basis of
such waveform. More specifically, after calculating the central
position of each of the patterns P.sub.1 to P.sub.5 on the basis of
the right and left edge positions, the FIA calculating unit 435
adds up the positions of the five linear patterns P.sub.1 to
P.sub.5 and divides the sum by 5, thereby detecting the mark
position in the X direction to serve as the center.
[0281] Then, the FIA calculating unit 435 calculates a difference
.DELTA.XF(=XR.sub.0-Xm) between the position XR.sub.0 which has
been obtained in advance and the mark measuring position Xm, and
supplies a value which is obtained by adding the difference AXF to
a position at which the wafer stage T is positioned to the main
control system 500 as mark position information AP2.
[0282] Further, in the FIA system 436, the illumination light of
the wafer W passing through the filter 423 illuminates a local area
(smaller than a shot area) including a wafer mark on the wafer W
with a substantially uniform intensity of illuminance, and the
wavelength range is determined to be 200 nm or around.
[0283] Then, the FIA system 436 is constituted by the components
from the halogen lamp 420 to the FIA calculating unit 435, in the
order of reference numeral. Since the light in the wavelength band
range of 200 nm or around passes through a telecentric image
forming optical system which comprises the objective lens 427, the
lens system 429, the relay systems 431 and 433X (or 433Y), it is
clearly required to compensate a color aberration corresponding
thereto. Further, it is preferable that the number of apertures
(N.A.) on the wafer side of the objective lens 427 be smaller than
the number of apertures of the projection optical system PL.
[0284] In the present embodiment, a part of an observation field
range of the objective lens 427 is slipped into a lower surface of
the lens barrel of the projection optical system PL by a prism 428
so as to be close to the field of view of the projection optical
system PL as much as possible. In general, a projection exposure
apparatus of this type is provided with a focus sensor for
detecting a gap (deviation) between an image forming plane of the
projection optical system PL and the surface of the wafer W
accurately, and a leveling sensor for detecting a relative
inclination between the plane of a shot area on the wafer W and the
image forming plane of the projection optical system PL. These
focus sensor and leveling sensor are arranged to apply a light flux
of infrared range in a slanting manner onto the wafer W in which
the projection field of the projection optical system PL exists and
to perform focusing and leveling in order to obtain a deviation in
a light-receiving position of the light reflected therefrom. In
this connection, if the number of apertures of the objective lens
427 is small, the depth of focus of the objective lens 427 is
deepened. If a focusing is effected based on a result of detection
by said focus sensor, the detection is performed also by the FIA
system 436 in an in-focus state.
[0285] In the structure shown in FIG. 19, since the center of
detection of the FIA system 436 of the off-axis system (a position
of a conjugate image at the center of the index plate 430) is
separated away from the center of the projection optical system PL,
Abbe's error (off-axial error caused by an inclination of the
stage) ia suppressed to the minimum by providing the center of
detection of said FIA system 436 on a straight line for connecting
the measurement position of the interferometer 412 to the center of
the projection optical system PL, i.e., on the length-measurement
axis (the center line of a length-measuring beam).
[0286] Moreover, in order to execute an alignment, it is required
to perform a search alignment for roughly positioning the wafer
(global alignment) and a fine alignment for performing an alignment
with a high accuracy. With respect to this search alignment, there
is also proposed a method of mixing the alignment system of the TTL
method and the alignment system of the off-axis method, as
disclosed in U.S. Pat. No. 4,677,301, for example. The apparatus of
this embodiment normally adopts a sequence for performing the
search alignment by detecting three or two alignment marks on the
wafer by the use of the LIA system 410 of the TTL method which has
a high processing speed. However, there are cases where the
alignment is not performed normally because of a wafer ground, or a
thickness or kind of the photoresist layer (specially when the mark
detection is not performed satisfactorily) so that there is also
provided means for switching the sequence to execute the search
alignment by using the FIA system 436 with an illumination
wavelength having a wide band range of the off-axis type. In this
case, the sequences are switched over by determining a mark
detection time, a size, a distortion, or the like of a mark
detection signal when the search alignment is executed by the LIA
system 410 of the TTL type.
[0287] Next, description will be made on the main control system
500 for integrally controlling the LIA system 410 of the TTL
method, the FIA system 436 of the off-axis system, the stage
controller 414, and the like. The main control system 500 is
arranged to always receive positional information PDS from the
interferometer 412. An alignment (ALG) data storing portion 501 is
capable of receiving both mark positional information AP.sub.1 from
the LIA calculating unit 409 and mark positional information
AP.sub.2 from the FIA calculating unit 435.
[0288] An EGA (enhanced global alignment) calculating unit 502
calculates an actual shot arrangement coordinate value on the
wafer, and a magnification (shot magnification) of a chip
parameter, and the like, by a statistic computation method based on
each mark positional information stored in the ALG data storing
portion 501. A result of said calculation is sent to a sequence
controller 506.
[0289] An exposure (EXP) shot map data portion 503 stores designed
values in the arrangement coordinate of four pairs of wafer marks
in each of all the shot areas to be exposed on the wafer, and these
designed values are sent to the EGA calculating unit 502 and the
sequence controller 506. An alignment shot map data portion 504
stores designed values in the arrangement coordinate of the four
pairs of wafer marks in each of all the shot areas (sample shots)
to be measured on the wafer, and these coordinate values are sent
to the EGA calculating unit 502 and the sequence controller 506. A
correction data storing portion 505 stores various kinds of data
for alignment, correction data for positioning an exposure shot, or
the like, and these kinds of correction data are sent to the ALG
data storing portion 501 or the sequence controller 506. The
sequence controller 506 determines a series of procedures for
controlling a movement of the wafer stage ST in the alignment mode
or the exposure mode of the step and repeat method.
[0290] Also, the projection optical system PL of this embodiment is
provided with an imaging characteristic control device 419. The
imaging characteristic control device 419 adjusts a projection
magnification and a distortion of the projection optical system PL
by adjusting a gap between predetermined lens groups out of the
lens groups constituting, for example, the projection optical
system PL, or adjusting a pressure of a gas inside a lens chamber
between predetermined lens groups. As a result, a magnification of
a projected image of the reticle is adjusted in accordance with a
shot magnification measured, for example, by the in-shot
multi-point EGA alignment. An operation of the imaging
characteristic control device 419 is also controlled by the
sequence controller 506.
[0291] Next, description will be made on a basic alignment sequence
of the present embodiment. Also in the present embodiment, a shot
area 27-n as shown in FIG. 13 is formed on the wafer W. As shown in
FIG. 13, four cross-shaped alignment marks 29 (n, N) (N=1 to 4) are
formed on each shot area 27-n on the wafer W. A reference position
is determined for each of the shot area 27-n. For example, assuming
that the reference position is determined to be the reference point
28-n at the center of the shot area 27-n, designed coordinate value
of this reference point 28-n in the coordinate system (.alpha.,
.beta.) on the wafer W is represented by (C.sub.Xn, C.sub.Yn) (see
FIG. 13). Also in this embodiment, pairs of wafer marks 29 (n, 1)
to 29 (n, 4) attached in each of shot area 27-n is actually
comprised of the wafer marks MX1 to MX4 for the X axis and the
wafer marks MY1 to MY4 for the Y axis, as described with reference
to FIG. 20A. For the convenience of explanation, the marks formed
in each shot area will be described as cross-shaped marks. In this
case, the centers of the cross-shaped marks are positioned on the
measuring points SC1 to SC4 in the shot area shown in FIG. 20A.
[0292] In this case, if a coordinate system (x, y) on the shot area
is set to be parallel to the coordinate system (.alpha., .beta.) on
the wafer W in FIG. 4A, as shown in FIG. 13, coordinate values upon
the design of the measuring points in the coordinate system (x, y)
corresponding to the paired wafer marks 29 (n, 1), 29 (n, 2), 29
(n, 3) and 29 (n, 4) are respectively represented by (S.sub.1Xn,
S.sub.1Yn), (S.sub.2Xn, S.sub.2Yn), (S.sub.3Xn, X.sub.3Yn) and
(S.sub.4Xn, S.sub.4Yn). For example, with respect to the paired
wafer marks 29 (n, 1), the X-coordinate S.sub.1Xn in the coordinate
(S.sub.1Xn, S.sub.1Yn) indicates the X-coordinate of the wafer mark
MX1 for the X axis, while the Y-coordinate (S.sub.1Yn) indicates
the Y-coordinate of the wafer mark MY1 for the Y axis.
[0293] In this embodiment, like the foregoing first and second
embodiments in which 10 error parameters contained in the
transformation matrices A, B and O in the coordinate transformation
in the equation (10) or (17) are obtained by using statistic
computation (e.g., by the method of least squares). In the present
embodiment, 10 error parameters contained in the transformation
matrices A, B and O in the coordinate transformation in the
equation (10) or (17) are obtained in the following manner.
[0294] The 10 error parameters (.THETA., W, .GAMMA.x (or Rx),
.GAMMA.y (or Ry), O.sub.X, O.sub.Y, .theta., wx (=rx-1), ry)
contained the transformation matrices A, B and O in the coordinate
transformation in the equation (17) are called in-shot multi-point
EGA parameters. Out of these 10 error parameters, four error
parameters indicating a status in a shot area, namely, the shot
magnifications .gamma.x (or rx), .gamma.y (or rx), and the shot
rotation .theta. and the chip rectangular degree w, are called the
in-shot parameters. The above-mentioned 10 in-shot multi-point EGA
parameters can be obtained by, for example, the method of least
squares. In this embodiment, errors in calculated coordinates in
the stage coordinate system (X, Y) and in each chip in each shot
area on the wafer W are obtained on the basis of the coordinate
transformation in the equation (17). Then, based on these errors,
an error in the shot rotation (chip rotation), an error in the shot
magnification (chip magnification), and the like, are compensated,
and thereafter, arrangement coordinates (F.sub.xn, F.sub.yn) upon
calculation of each shot area 27-n on the wafer W are calculated.
On the basis of this coordinates, alignment between each shot area
27-n and the reticle is performed so as to expose the pattern image
of the reticle.
[0295] Here, the above-mentioned process will be described with
reference to the corresponding components in the main control
system 500 shown in FIG. 19. In this main control system 500, the
arrangement coordinates values upon the design of the four paired
wafer marks in all of the shot areas on the wafer are stored in the
EXP shot map data portion 503, while the coordinates values upon
the design of the four paired wafer marks in the sample shot areas
are stored in the ALG shot map data portion 504. Then, the
calculation equation of the approximation of least squares for
determining the above-mentioned 10 in-shot multi-point EGA
parameters is stored in the EGA calculating unit 502.
[0296] It is noted that the method of least squares is not
necessarily applied to the equation (17). Instead, the 10 in-shot
multi-point EGA parameters may be obtained in the step of the
equation (15).
[0297] The above-mentioned equation (16) contains all of the four
in-shot parameters regarding the chip pattern (i.e., the shot
rotation .theta., the chip rectangular degree w, and the shot
magnifications rx (=1+.gamma.x), ry (=1+.gamma.y)). However, it is
possible to employ the equation (16) (or the equation (15)) by
giving attention to any one parameter out of these four. More
specifically, when attention is given only to the shot rotation
.theta., the equation (16) is employed by considering the chip
rectangular degree w to be zero, and the shot magnifications rx and
ry as 1, respectively. With regard to this, it is also possible to
employ the equation (16) when attention is given to the shot
magnifications rx and ry, assuming that rx=ry, that is, the linear
expansion and contraction are isotropic.
[0298] A parameter to which an attention is to be given may be
selected out of the four in-shot parameters in accordance with a
kind (characteristics) of a wafer to be exposed.
[0299] Here, it is assumed that a wafer mark should be measured
with respect to a sample shot which has been selected in advance
out of all of the shot areas 27-n of the wafer W. However, since a
distance between the reference point 28-n of each sample shot and
the wafer mark in said shot area is comparatively short, there
generate large errors due to the reproductivity of measurement, or
the like, with respect to the four in-shot parameters (.theta., w,
rx and ry) out of the above-mentioned 10 in-shot multi-point EGA
parameters. For this reason, in order to reduce the errors, the
number of sample shots and the number of wafer marks to be measured
must be comparatively large. However, in this case, a through-put
of the exposure process is lowered. Then, in the present
embodiment, the decrease of the through-put is prevented and the
alignment accuracy is kept high by using the following sequence.
The following process utilizes the fact that an amount of linear
error and an amount of non-linear error generally generated on the
wafer and a deformation in a chip pattern in each shot area have
the same tendencies in the same lot.
[0300] Also in the present embodiment, since there are provided two
alignment sensors, two types of 10 in-shot multi-point EGA
parameters can be obtained by an alignment sensor for detecting
coordinate values of each wafer mark in a sample shot. More
specifically, when an alignment of the EGA method is executed on
the basis of a result of measurement by the LIA system 10, it is
possible to obtain the 10 in-shot multi-point EGA parameters which
includes the scaling .GAMMA.x and .GAMMA.y, the shot magnifications
.gamma.x and .gamma.y, the shot rotation .theta., and the chip
rectangular degree w in (Numerical Formula 10). In the same manner,
when an alignment of the EGA method is executed on the basis of a
result of the measurement by the FIA system 36, the 10 in-shot
multi-point EGA parameters of the equation (27) can be obtained.
However, some of the parameters obtained on the basis of the result
of the measurement by, for example, the LIA system 410 may have
predetermined deviations. Then, such a deviant parameter is
corrected by a transformation parameter which is obtained based on
a result of the measurement by the FIA system 436 and is used.
[0301] Next, an operation of an exposure using an alignment of the
in-shot multi-point EGA method with respect to a wafer in one lot
in the present embodiment will be described below with reference to
a flowchart in FIG. 18. The following operation is executed when an
exposure is effected onto a predetermined circuit pattern layer
(process layer) on the wafer. On said process layer, errors having
substantially the same tendencies, that is, predetermined
deviations from correct values are mixed in the scaling Rx and Ry
and the shot magnifications rx and ry (or .gamma.x and .gamma.y)
out of the in-shot multi-point EGA parameters which is obtained on
the basis of a result of measurement by the alignment sensor of the
LIA method from results of experiments and evaluation at trial in
advance. However, errors in the other parameters are small. On the
other hand, it is understood that errors in the scalings Rx and Ry
and the shot magnifications rx and ry out of the in-shot
multi-point EGA parameters which are obtained on the basis of a
result of the measurement by the alignment sensor of the FIA method
are small.
[0302] First, the first alignment sequence of the in-shot
multi-point EGA method using the LIA system 410 and the second
alignment sequence of the in-shot multi-point EGA method using the
FIA system 436 are stored in the main control system 500, and an
arrangement of sample shots (wafer marks, to be correct) to be
measured on the wafer is set in the same manner by the first and
second alignment sequences. Then, the in-shot multi-point EGA
parameters obtained by the first alignment sequence are basically
used. However, only the scalings Rx and Ry and the shot
magnifications rx and ry out of said parameters are corrected in
the following manner on the basis of the in-shot multi-point EGA
parameters obtained by the second alignment sequence.
[0303] More specifically, at step 301 shown in FIG. 18, the first
wafer W in one lot is loaded onto the wafer stage ST in FIG. 19. In
this case, since an alignment of the reticle R has been completed,
amounts of deviations of the reticle R in the X and Y directions
and the direction of rotation with respect to the rectangular
coordinate system which is specified by an unrepresented
interferometer are substantially zero.
[0304] FIG. 23 shows a wafer W to be exposed. Referring to this
FIG. 23, though a lot of shot areas are arranged on the wafer W
along a coordinate system (sample coordinate system) (.alpha.,
.beta.) on the wafer W, only sample shots 27-1 to 27-8 to be
measured are illustrated. In the shot area 27-n (n=1 to 8), four
paired wafer marks 29 (n, 1) which are the same as the paired wafer
marks 29 (n, 1) in FIG. 20A are respectively formed. After that, at
step 302, a search alignment (global alignment) is executed. More
specifically, a several number of alignment marks for rough
positioning are formed along the sample coordinate system (.alpha.,
.beta.) separately from the wafer marks attached in each shot area.
Then, coordinate values of these alignment marks in the stage
coordinate system (static coordinate system) (X, Y) are measured
by, for example, the LIA system 410 (including an LIA system for
the Y axis, the same is applied to the followings) or the FIA 436
in FIG. 19. Transformation parameters (scaling, rotation, offset,
etc.) which are approximated to the stage coordinate system (X, Y)
from the sample coordinate system (.alpha., .beta.) are obtained
based on a result of said measurement and are stored in a memory of
the EGA calculating unit 502 inside the main control system
500.
[0305] After that, when an alignment of the in-shot multi-point EGA
method is performed, coordinate values of said paired wafer marks
in the stage coordinate system (X, Y) are calculated in the EGA
calculating unit 502 based on the arrangement coordinates in the
sample coordinate system (.alpha., .beta.) at the reference point
in a shot area to be measured, arrangement coordinates of each
paired wafer mark having said reference point as the original
point, and transformation parameters approximated thereto. These
coordinate values are supplied to the stage controller 414 via the
sequence controller 506. Then, on the basis of these supplied
coordinate values, the wafer marks for the X axis and the Y axis
out of the paired wafer marks to be measured are successively moved
to an observation field of the FIA system 436 or a laser beam
irradiation area from the LIA system 410.
[0306] Next, at step 303 in FIG. 18, an alignment of the in-shot
multi-point EGA method is executed by using the LIA system 410 of
the TTL method. In other words, coordinate values (FM.sub.NXn,
FM.sub.NYn) on the stage coordinate system (X, Y) of the paired
wafer marks (29 (1, 1) 29 (1, 4) to 29 (8, 1) . . . , 29 (8, 4)) in
all of the sample shots 27-1 to 27-8 on the wafer W in FIG. 23 are
actually measured by the LIA system 410 (including the LIA system
for the Y axis), which means all of the paired wafer marks in all
of the sample shots on the wafer W are to be subjected to the
measurement. However, it is not necessary to measure all of the
wafer marks in all of the sample shots. Since two one-dimensional
wafer marks are provided for one pair of wafer marks, it is
necessary to actually measure the coordinate values of at least
five paired wafer marks in order to determine 10 or more parameter
values. However, it is possible to select to measure the wafer
marks for the X axis only with respect to some paired marks, and to
measure the wafer marks for the Y axis only with respect to the
other paired wafer marks.
[0307] In this case, the arrangement coordinate values (C.sub.Xn,
C.sub.Yn) upon the design of the reference mark 28-n (see FIG. 13)
on the coordinate system (.alpha., .beta.) on the wafer W and the
coordinate values upon design (relative coordinate values)
(S.sub.NXn, S.sub.NYn) of the measured paired wafer marks 29 (n, N)
(N=1 to 4) on the coordinate system (x, y) in each sample shot 27-n
are obtained in advance. Then, at step 303, the arrangement
coordinate values upon the design (C.sub.Xn, C.sub.Yn) of the
reference mark in the shot area to which the measured alignment
mark belongs and the relative coordinate values upon the design
(S.sub.NXn, S.sub.NYn) related to the reference point of said
alignment mark are substituted for the right side of the equation
(17) so as to obtain coordinate values (F.sub.NXn, F.sub.NYn) upon
calculation of said paired wafer mark 29 (n, N) to be in the stage
coordinate system (X, Y).
[0308] Then, the 10 in-shot multi-point EGA parameters (hereinafter
called the "LIA parameters") to satisfy the equation (17) by a
calculation by the method of least squares by the EGA calculating
unit 502 are calculated. These LIA parameters includes the scaling
.GAMMA.x (or Rx) and scaling .GAMMA.y (or Ry), the rotation
.THETA., the rectangular degree W, the offsets Ox, Oy, the shot
magnifications .gamma.x (or rx) and .gamma.y (or ry), the shot
rotation .theta., and the chip rectangular degree w.
[0309] More specifically, a difference (E.sub.NXn, E.sub.NYn)
between the coordinate values (FM.sub.NXn, FM.sub.NYn) measured
actually and the coordinate values upon calculation (FN.sub.NXn,
F.sub.NYn) thereof is considered as an alignment error. As a
result, E.sub.NXn=FM.sub.NXn-F.sub- .NXn,
E.sub.NYn=F.sub.NYn"F.sub.NYn is satisfied. Then, if such an
equation in which a square sum of the alignment errors (E.sub.NXn,
E.sub.NYn) related to the measured alignment mark are partially
differentiated with each of these 10 parameters successively and
each of the obtained values becomes zero is set up, and if these 10
simultaneous equations are solved, the 10 parameters can be
obtained.
[0310] After that, at step 304, the coordinate values in the stage
coordinate system (X, Y) of each paired wafer mark 29 (n, N) in
each of the sample shots 27-1 to 27-8 on the wafer W shown in FIG.
18 are measured by using the FIA system 436 to execute an alignment
of the in-shot multi-point EGA method. The measured values obtained
in this step are processed by the EGA calculating unit 502 so as to
calculate the 10 in-shot multi-point EGA parameters (hereinafter
called the "FIA parameters"). These FIA parameters also comprise
the scaling .GAMMA.x (or Rx) and scaling .GAMMA.y (or Ry), the
rotation .THETA., the rectangular degree w, the offsets O.sub.x,
O.sub.y, the shot magnifications .gamma.x (or rx) and .gamma.y (or
ry), the shot rotation .theta., and the chip rectangular degree
w.
[0311] At the next step 305, with respect to the ordinary EGA
parameters (the parameters related to the wafer) including the
scaling .GAMMA.x (or Rx) and scaling .GAMMA.y (or Ry), the rotation
.THETA., the rectangular degree W, and the offsets O.sub.x, O.sub.y
out of the obtained 10 in-shot multi-point EGA parameters, a
difference .DELTA..GAMMA.x.sub.FL (or .DELTA.R.sub.XFL),
.DELTA..GAMMA.y.sub.FL (or .DELTA.Ry.sub.FL) .DELTA..THETA..sub.FL,
.DELTA.W.sub.FL, .DELTA.O.sub.XFL, and .DELTA.O.sub.YFL, each of
which is obtained by subtracting the LIA parameter from the FIA
parameter, are calculated, and these obtained differences are
stored in a correction data storing portion 505 inside the main
control system 500. Further, with respect to the shot
magnifications .gamma.x (or rx) and .gamma.y (or ry), the shot
rotation .theta., and the chip rectangular degree w which are the
in-shot parameters out of the in-shot multi-point EGA parameters,
the LIA-parameters and FIA parameters themselves are stored in the
correction data storing portion 505.
[0312] Then, for the wafer W for which the measurement is effected,
at step 306, values of the LIA parameters are used for the offsets
O.sub.x, O.sub.y, the rotation .THETA., the rectangular degree W,
the chip rectangular degree w and the shot rotation .theta., while
the scaling .GAMMA.x (or Rx) and scaling .GAMMA.y (or Ry) and the
shot magnifications .gamma.x (or rx) and .gamma.y (or ry), values
of the FIA parameters are used. Then, an appropriate rotation is
applied to the reticle R via the reticle stage RS in FIG. 19 so as
to correct the rotation .THETA. of the wafer in the transformation
matrix A in the equation (17) and the shot rotation .theta. in the
transformation matrix B, or the wafer W is rotated so as to correct
a rotation of a chip pattern for the stage coordinate system (X,
Y), which means that the reticle R or the wafer W is rotated in
accordance with a sum (.THETA.+.theta.) of the rotation .THETA. for
constituting an element of the transformation matrix A and a shot
rotation .theta. for constituting an element of the transformation
matrix B in the equation (27).
[0313] However, when the wafer W is rotated, there is a possibility
that the offsets (O.sub.x, O.sub.y) of the wafer may change, it is
required to re-calculate error parameters by performing a
calculation (an in-shot multi-point EGA calculation) for obtaining
parameters by the above-mentioned method of least squares after the
coordinate values of the wafer mark are remeasured. That is, when
the wafer W is rotated only by the angle (.THETA.+.theta.), it is
required to repeat the above-mentioned processes at steps 303 to
306, which also means to confirm whether or not a new rotation
.THETA. after the rotation of the wafer W is a value corresponding
to the angle of rotation at step 306.
[0314] The chip rectangular degree w can not be corrected in a
strict sense. However, an error in said chip rectangular degree w
can be suppressed to be small by rotating the reticle R properly.
Then, it is possible to optimize an amount of rotation of the
reticle R or the wafer W such that respective sums of absolute
values of the rotation .THETA., the shot rotation .theta. and the
chip rectangular degree w are minimized.
[0315] Next, a projection magnification of the projection optical
system PL is adjusted via the imaging characteristic control device
419 in FIG. 19 in such a manner that the shot magnifications
.gamma.x (or rx) and .gamma.y (or ry) in the transformation matrix
B in the equation (17) are corrected, which means that the
projection magnification of the projection optical system PL is
adjusted in accordance with the shot magnifications .gamma.x
(=rx-1) and .gamma.y (=ry-1) for constituting elements of the
transformation matrix B in the equation (27).
[0316] Thereafter, the transformation matrices A and O containing
the elements comprising the in-shot multi-point EGA parameters
obtained at step 305 are used to substitute the arrangement
coordinate values upon the design (C.sub.Xn, C.sub.Yn) of the
reference point 28-n in each shot area 27-n on the wafer W for the
following equation so as to obtain the arrangement coordinate
values (G.sub.Xn, G.sub.Yn) upon calculation of said reference
point 28-n in the stage coordinate system (X, Y).
[0317] At step 307, arrangement coordinates which are calculated on
the basis of the arrangement coordinate system (G.sub.Xn, G.sub.Yn)
obtained at step 306 and an amount of a base line (a distance
between the center of detection of an alignment sensor and the
center of exposure) which has been obtained in advance are
successively supplied to the stage controller 414 via the sequence
controller 506. Then, the reference point 28-n of each shot area
27-n on the wafer W is aligned with the center of an exposure field
of the projection optical system PL shown in FIG. 19 so as to
perform a projection-exposure of a pattern image of the reticle R
onto said shot area 27-n. As a result, the program advances to step
308 upon completion of the exposure onto all of the shot areas on
the wafer W.
[0318] At step 308, the exposed wafer W is conveyed, and the i-th
(i=2, 3, . . . ) wafer to be exposed next in the same lot is loaded
onto the wafer stage ST in FIG. 19.
[0319] In this embodiment, on the assumption that process status in
the same lot has no large difference, a deviation (process offset)
mixed into the scaling .GAMMA.x (or Rx) and the scaling .GAMMA.y
(or Ry) out of the LIA parameters which are obtained on the basis
of the measurement results by the LIA system 410 has substantially
a constant value in the one lot. Further, the shot magnifications
.gamma.x (=rx-1) and .gamma.y (=ry-1), and the shot rotation are
considered to have substantially constant values.
[0320] Then, with respect to the second and subsequent wafers, the
ordinary alignment of the EGA method is performed by using only the
LIA system 410, the scaling out of the obtained LIA parameters is
corrected by using the difference obtained for the first wafer, and
for the shot rotation and the shot magnification the values
obtained and stored for the first wafer are used.
[0321] Accordingly, as a sequence, after the search alignment is
executed at step 309 in the same manner as that at step 302, the
flow moves to the step 310 to measure the coordinate values of, for
example, the first paired wafer marks 29 (1, 1) to 29 (8, 1) only
with respect to the sample shots 27-1 to 27-8 having the same
arrangement as those on the i-th wafer in FIG. 23 by using the LIA
system 410, and a result of this measurement is processed to
calculate the values for the ordinary EGA parameters (LIA
parameters). In this case, the values for the LIA parameters
obtained at the following step 311 are used for the wafer W
measured at this st, while the values for the LIA parameters
obtained immediately before are used for the offsets Ox and
O.sub.y, the rotation .THETA. and the rectangular degree W. Values
which are obtained by adding the scaling differences
.DELTA..GAMMA.x.sub.FL (or .DELTA.Rx.sub.FL) and
.DELTA..GAMMA.y.sub.FL (or .DELTA.Ry.sub.FL) stored at step 305 to
the LIA parameter values obtained immediately before are used for
the scaling .GAMMA.x (or Rx) and the scaling .GAMMA.y (or Ry), the
LIA parameter values stored at step 305 are used for the shot
rotation .theta. and the chip rectangular degree w, and the FIA
parameter values stored at step 305 are used for the shot
magnification .gamma.x (or rx) and .gamma.y (or ry).
[0322] Though all of the parameter values are determined in this
manner, the values for the shot rotation and the shot magnification
are corrected with respect to the first wafer so that there is no
special need for performing correction with respect to the second
and subsequent wafers. However, with respect to the rotation
.THETA., the correction may be performed by rotating the wafer or
the reticle R.
[0323] After that, the transformation matrices A and O which
contain the elements comprising these in-shot multi-point EGA
parameters are used to substitute arrangement coordinate values
(C.sub.Xn, C.sub.Yn) upon the design of the reference point 28-n in
each shot area 27-n on the wafer for the equation (28) in the EGA
calculating unit 505. Thus, the arrangement coordinate values
(G.sub.Xn, G.sub.Yn) upon calculation in the stage coordinate
system (X, Y) of said reference point 28-n can be obtained.
[0324] At step 312, the arrangement coordinates (G.sub.Xn,
G.sub.Yn) obtained at step 311 and the arrangement coordinates to
be obtained on the basis of the amount of base line which has been
obtained in advance are successively supplied to the stage
controller 314 via the sequence controller 506 so as to align the
reference point 28-n in each shot area 27-n on the wafer W with the
center of the exposure field of the projection optical system PL
shown in FIG. 19, successively. Thus, a pattern image of the
reticle R is projection-exposed onto said shot area 27-n.
[0325] Next, at step 313, it is determined whether there is a wafer
to be exposed residual in this lot or not. If there is one, the
steps 308 to 312 are repeated to perform alignment and exposure. If
there is no residual wafer to be exposed at step 313, this process
is completed.
[0326] As described above, in the present embodiment, since the
alignment is performed by the in-shot multi-point EGA method by
using the LIA system 410 and the FIA system 436, not only the
alignment accuracy between the shot areas, but also the alignment
accuracy in a shot area such as that of the shot rotation and, shot
magnification, etc., can be advantageously improved. However,
taking into consideration that the in-shot parameters have the same
tendencies in one lot, only the first wafer is required for the
measurement by the in-shot multi-point EGA method actually. With
respect to the subsequent wafers, measured values, stored values or
values corrected with the stored values are used so that the
through-put is hardly lowered, compared with that in the alignment
by the ordinary EGA method.
[0327] It is noted that, in the foregoing description, the sample
shots are measured respectively by the FIA system 436 and the LIA
system 410 only for the first wafer in a lot in order to obtain a
difference between an FIA parameter and an LIA parameter and
in-shot parameters (shot magnification, shot rotation, and chip
rectangular degree). However, with respect to the first several
wafers, the alignment by the in-shot multi-point EGA method and the
alignment by the in-shot multi-point parameter method may be
performed by using the LIA system 410 and the FIA system 436,
respectively, so as to obtain an average of the LIA parameters and
an average of the FIA parameters for said several wafers or a
difference between said averages.
[0328] Then, with respect to subsequent wafers, the LIA system 410
which is capable of a high through-put may be used to perform
alignment by the in-shot multi-point EGA method. In this case, with
respect to the parameters (the scaling, and the shot magnification)
which may have deviations in the LIA system 410, a high through-put
and high alignment accuracy can be obtained by correcting said
deviations with the difference between the average of the FIA
parameters and that of the LIA parameters which have been already
calculated.
[0329] Also, like at steps 303 and 304 in FIG. 18, the number of
sample shots for calculating correction values for the in-shot
multi-point EGA parameters may be large, compared with the number
of ordinary sample shots as to be measured at step 310 in FIG.
18.
[0330] The two-dimensional coordinate values of one point in each
sample shot (the X-coordinate and the Y-coordinate of one paired
wafer mark) are measured by the LIA system 410 with respect to any
of the second and subsequent wafers in the above description.
Though the measurement of the ordinary EGA method is performed by
using the LIA system 410 capable of a high through-put with respect
to any of the second and subsequent wafers (or the third or fourth
and subsequent wafers), the Y-coordinate of one wafer mark for the
Y axis which has a different position in the X direction in each
sample shot may be measured by the LIA system 410 or the FIA system
436, together with said ordinary measurement. For example, in FIG.
23, the Y-coordinate of the paired wafer mark 29 (1, 2) or 29 (1,
3) in each of the sample shots 27-1 to 27-8 is measured by using
LIA system 410, while the X-coordinate and the Y-coordinate of one
of the paired wafer marks 29 (1, 1) to 29 (8, 1) in each of the
sample shot 27-1 to 27-8 are measured by using the LIA system
410.
[0331] In this case, since a multi-point measurement is performed
with respect to the Y axis in each sample shot, the shot rotation
.theta. which is one of the in-shot parameters out of the in-shot
multi-point EGA parameters can be obtained. Then, at a step
corresponding to the step 311 in FIG. 18, the value for the shot
rotation which is obtained immediately before is used for the shot
rotation .theta., and the reticle R or the wafer W is rotated in
accordance with a sum (.THETA.+.theta.) which is obtained by adding
the value for the rotation .THETA. for constituting an element of
the transformation matrix A in the equation (27) to the shot
rotation .theta. obtained immediately before constituting an
element of the transformation matrix B. After that, the exposure is
effected so that the exposure is effected in a state in which a
rotation error between the reticle R and each shot area on the
wafer W is small.
[0332] Further, in addition to the measurement of one paired wafer
marks by using the LIA system 410 in each sample shot, the
X-coordinate of the paired wafer marks which have substantially the
same Y-coordinate may be measured by using the FIA system 436.
Thereby, the shot magnification .gamma.x (or rx), .gamma.y (or ry)
serving as in-shot parameters can be obtained. However, there
arises no substantial inconvenience if the FIA parameter value
which is measured and stored for the wafers up to the fourth or
fifth wafer is used for the shot magnification. This is because the
shot magnification is normally stable in a lot, while the shot
rotation is sometimes different for each wafer.
[0333] In the present embodiment, as shown in FIG. 20B, the paired
wafer marks 29 (n, 1) to 29 (n, 4) which comprise one-dimensional
wafer marks arranged in the X and Y directions in the stage
coordinate system are provided at the four corners on the diagonal
lines in the shot area 27-n. However, if, for example, four paired
wafer marks are designed not to be arranged on one straight line,
the above-mentioned arrangement is not always required. Further,
the number of paired wafer marks may be two or more. Also, the
position of the wafer mark for the X axis may be different from
that for the Y axis.
[0334] Furthermore, a two-dimensional mark having, for example, a
cross-shaped pattern may be used, depending on a combination of
alignment sensors to be used.
[0335] It is not required to form wafer marks inside each shot area
27-n. Wafer marks may be formed at predetermined positions on a
street line area SCL between the shot area 27-n and an adjacent
shot area, for example, in FIG. 20A.
[0336] In the above embodiment, the FIA system 436 in FIG. 19 is of
the off-axis method, while the LIA system 410 of the TTL method.
However, the FIA system 436 may be used by, for example, the TTL
method or the TTR method. In the opposite way, the LIA system 410
may be used by the TTR method. In the above embodiment, the LIA
system 410 and the FIA system 436 are used as alignment sensors.
However, an alignment sensor of the laser step alignment (LSA)
method for relatively scanning the wafer marks and the laser beams
which is converged in a slit-like form and the like may be used, in
addition.
[0337] Further, in the present embodiment, a method for treating
the wafer marks in each sample shot equally is employed as the
in-shot multi-point EGA method. However, it is possible to employ a
weighing method in which a value of a transformation parameter is
determined in such a manner that a residual error component which
can be obtained by applying a weight determined in accordance with
a distance from, for example, the center of the wafer with respect
to each wafer mark in a sample shot on the wafer is minimized.
[0338] As described, the present invention is not limited to the
foregoing embodiments, but can take various configurations within a
scope of the concept of the present invention.
* * * * *