Method of detecting coma of projection optical system

A method of detecting coma of a projection optical system includes receiving an image of a pattern projected by the projection optical system, at at least one position along an optical axis of the projection optical system, detecting a position of at least one received pattern image, with respect to a plane perpendicular to the optical axis of the projection optical system, and determining coma of the projection optical system on the basis of the detection.

FIELD OF THE INVENTION AND RELATED ART 
This invention relates to a method of detecting coma of a projection 
optical system. The invention is applicable, for example, to measurement 
of aberration of a projection optical system, particularly coma thereof, 
for projecting an electronic circuit pattern of a reticle onto a wafer in 
the manufacture of semiconductor devices such as ICs or LSIs, for example, 
in order to reduce the effect of such aberration and to ensure high 
resolution imaging of the circuit pattern upon the wafer. 
For the manufacture of semiconductor devices such as ICs or LSIs, in many 
cases, a projection exposure apparatus (aligner) is used since it 
relatively easily attains high resolution and high throughput. In such a 
projection exposure apparatus, a wafer is moved every time one exposure 
process is completed and then another zone of the wafer is exposed. Such 
an exposure process is repeated sequentially so that images of an 
electronic circuit pattern are printed on the whole surface of the wafer. 
This is called a "step-and-repeat exposure method". 
In this process, a projection optical system serves to project the 
electronic circuit pattern of a reticle onto the wafer surface in a 
reduced scale corresponding to a predetermined projection magnification 
such as 1:5 or 1:10, for example. Here, the image quality (projection 
resolution) of the image of the circuit pattern printed on the wafer is 
largely dependent upon the performance (aberration) of the projection 
optical system. One of the aberrations determining the performance of the 
projection optical system is coma. Proposals have been made in connection 
with how to measure coma of a projection optical system. Examples are as 
follows: 
(a) A method wherein an interferometer is used to measure wavefront 
aberration to determine coma (wavefront aberration measurement method). 
(b) A method wherein a pattern image is printed on a resist of a wafer and, 
after development, coma is determined on the basis of the shape of the 
printed pattern (resist pattern) (e.g. a difference in angle of walls of a 
projected image having a rectangular shape, for example) (printing 
method). 
Such a wavefront aberration measurement method using an interferometer 
needs specific environmental conditions for the measurement, such as 
keeping constant environmental temperature or avoiding fluctuation of air, 
for example. Also, it needs a complicated measuring system and processing 
system. Thus, the measuring device as a whole is large. 
Further, for the measurement, it is a requisition to place a lens system 
(projection optical system), to be examined, very precisely within the 
measuring device, and it takes a long working time. Additionally, a 
wavefront aberration measuring device itself is not widely used. Every 
user of a projection exposure apparatus may not possess such a measuring 
device, although every manufacturer of a projection exposure apparatus may 
have such a measuring device. It means a difficulty in performing the 
measurement in a factory in which the projection exposure apparatus is 
used. 
On the other hand, in the printing method in which coma of a projection 
optical system is determined on the basis of the shape of a resist 
pattern, generally an SEM (scanning electron microscope: an example is the 
S62.90 (trade name) available from Kabushiki Kaisha Hitachi Seisakusho) is 
used to take a photograph of a section, and coma is determined from a 
difference in angle of the walls. However, this method needs a long 
measurement time and the precision is not good. 
SUMMARY OF THE INVENTION 
It is accordingly an object of the present invention to provide a coma 
detecting method by which coma of a projection optical system is detected 
very simply. 
It is another object of the present invention to provide a coma correcting 
method by which coma of a projection optical system is corrected very 
simply. 
It is a further object of the present invention to provide a projection 
exposure apparatus in which degradation of resolution due to coma is 
reduced significantly. 
It is a yet further object of the present invention to provide a device 
manufacturing method in which degradation of resolution due to coma is 
reduced significantly. 
In accordance with an aspect of the present invention, there is provided a 
method of detecting coma of a projection optical system, said method 
comprising the steps of: receiving an image of a pattern projected by the 
projection optical system, at at least one position along an optical axis 
of the projection optical system; detecting a position of at least one 
received pattern image, with respect to a plane perpendicular to the 
optical axis of the projection optical system; and determining coma of the 
projection optical system on the basis of said detection. 
in one preferred form of this aspect of the present invention, a single 
pattern formed on a reticle is projected by the projection optical system, 
and images of the single pattern are received sequentially at different 
positions along the optical axis of the projection optical system. 
In accordance with another aspect of the present invention, there is 
provided a method of detecting coma of a projection optical system, said 
method comprising the steps of: providing patterns at different positions 
along an optical axis of the projection optical system; receiving images 
of the patterns projected by the projection optical system; detecting 
positions of the received pattern images with respect to a plane 
perpendicular to the optical axis of the projection optical system; and 
determining coma of the projection optical system on the basis of said 
detection. 
In one preferred form of this aspect of the present invention, the patterns 
are formed at upper and lower levels defined at the surface of a reticle, 
and wherein images of the patterns as projected by the projection optical 
system are received. 
In one preferred form of the first or second aspect of the present 
invention, a reference pattern defined on the or a reticle is projected by 
the projection optical system, wherein an image of the reference pattern 
is received and recorded at different positions on an image plane of the 
projection optical system and on the substrate, wherein the pattern images 
are received and recorded at positions on the substrate adjacent to the 
reference pattern image receiving position, and wherein the position of 
each pattern image with respect to the position of a corresponding 
reference pattern image is detected. 
In accordance with one preferred form of the first or second aspect of the 
present invention, a reference pattern defined on the or a reticle is 
projected by the projection optical system, wherein an image of the 
reference pattern is received upon an image plane of the projection 
optical system and by the photoelectrically converting means, wherein the 
position of the received image is memorized, wherein the pattern images 
are received by the photoelectrically converting means and at positions 
adjacent to the reference pattern image receiving position, wherein the 
positions of the received pattern images are memorized, and wherein the 
position of each pattern image with respect to the position of a 
corresponding reference pattern image is detected. 
In accordance with a further aspect of the present invention, there is 
provided a method of correcting coma of a projection optical system, said 
method comprising the steps of: detecting coma of the projection optical 
system in accordance with any one of the methods described above; and 
tilting at least one of lenses of the projection optical system with 
respect to an optical axis of the projection optical system, so as to 
reduce the coma. 
In accordance with a yet further aspect of the present invention, there is 
provided a method of correcting coma of a projection optical system, said 
method comprising the steps of: detecting coma of the projection optical 
system in accordance with any one of the methods described above; and 
shifting an optical axis of at least one of the lenses of the projection 
optical system, off an optical axis of the projection optical system, so 
as to reduce the coma. 
In accordance with a yet further aspect of the present invention, there is 
provided a method of correcting coma of a projection optical system, said 
method comprising the steps of: detecting coma of the projection optical 
system in accordance with any one of the methods described above; and 
tilting a parallel flat plate, disposed on a light path of the projection 
optical system, so as to reduce the coma. 
The coma correcting methods described above may be used in any combination. 
In one preferred form of these aspects of the present invention, the 
parallel flat plate comprises a sheet glass provided to seal at least one 
element of the projection optical system. 
In one preferred form of these aspects of the present invention, the 
parallel flat plate is disposed at an image side of the projection optical 
system. 
In one preferred form of these aspects of the present invention, the 
parallel flat plate is disposed at an object side of the projection 
optical system. 
In accordance with a further aspect of the present invention, there is 
provided a projection exposure apparatus, characterized in that: a pattern 
of a mask is projected on a substrate through a projection optical system, 
wherein coma of the projection optical system is corrected in accordance 
with any one of the coma correcting methods described above. 
In accordance with a yet further aspect of the present invention, there is 
provided a projection exposure apparatus for projecting a pattern of a 
mask onto a substrate through a projection optical system, characterized 
by: coma changing means for changing coma of the projection optical system 
so as to reduce the same; and detecting means for detecting coma of the 
projection optical system. 
In one preferred form of this aspect of the present invention, said coma 
changing means includes at least one of a lens element and a parallel flat 
plate, wherein said lens element is adapted to be tilted and/or 
translated, and wherein said parallel flat plate is adapted to be tilted. 
In accordance with a still further aspect of the present invention, there 
is provided a projection exposure apparatus for projecting a pattern of a 
mask onto a substrate through a projection optical system, characterized 
by inclusion of detecting means for detecting coma of the projection 
optical system. 
In accordance with a yet further aspect of the present invention, there is 
provided a device manufacturing method for printing a device pattern on a 
workpiece by use of any one of the projection exposure apparatuses 
described above.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In a first embodiment of the present invention, briefly, a pattern for 
detection of coma formed on a reticle is projected by a projection optical 
system on a resist, applied to a wafer, in a reduced scale. Here, pattern 
images (resist patterns) are formed at different positions along the 
focusing direction of the projection optical system (i.e., along the 
optical axis of the projection optical system), and the position of each 
resist pattern in a plane perpendicular to the optical axis is measured. 
Then, from the positional information of the resist patterns, coma of the 
projection optical system is detected. 
Initially, a description will be made of the relationship between the 
amount of shift of a pattern image and the amount of coma, which relation 
should be predetected for detection of coma from the positional 
information of resist patterns at different positions with respect to the 
focusing direction of the projection optical system. 
FIG. 2 illustrates how the amount of image shift as represented by .DELTA.d 
(nm) (which bears positional information of the resist pattern) changes 
with the amount of coma, when the position of the wafer surface with 
respect to the image plane (imaging position) of a projection optical 
system (N.A.=0.52) is changed along the focusing direction sequentially. 
The drawing of FIG. 2 shows the results of a simulation made with respect 
to four cases of coma 0, 0.1.lambda., 0.2 .lambda.and 0.5 
.lambda.(.lambda. is the wavelength of exposure light). 
In this embodiment, a simulation such as illustrated in FIG. 2 is performed 
beforehand with respect to many cases of coma, and a graph is prepared. 
Then, a curve of a image shift amount .DELTA.d of a resist pattern where 
the wafer surface position is changed sequentially along the focusing 
direction, is determined. From the relation between the thus obtained 
curve and the graph of FIG. 2, the amount of coma of the projection 
optical system is detected. 
FIG. 1 is schematic view of a first embodiment of the present invention, 
wherein the method of the present invention for detecting coma of a 
projection optical system is applied to a semiconductor device 
manufacturing projection exposure apparatus. 
In this embodiment, the amount of coma of a projection optical system 6 of 
the projection exposure apparatus in FIG. 1 is detected on the basis of 
the graph of FIG. 2. 
Now, components of the FIG. 1 apparatus will be explained. In FIG. 1, light 
emitted from an illumination system 9 irradiates a reticle 7 (first 
object) which is placed on a reticle stage 8. The projection optical 
system 6 projects an electronic circuit pattern formed on the reticle 7 
onto a wafer 3 (second object). The surface of the wafer 3 is coated with 
a resist (photosensitive material), and the wafer is held fixed on a 
movable stage (X-Y-Z stage) 2 which is mounted on a base 1. By means of a 
driving system (not shown), the movable stage 2 can be moved in X and Y 
directions as well as in a Z direction (along the optical axis of the 
projection optical system 6). The amount of movement of the movable stage 
in the X, Y and Z directions is monitored through X-axis and Y-axis 
mirrors 4 and laser distance measuring devices 5 as well as a level 
measuring means. In FIG. 1, only the laser distance measuring device 5 for 
the X-axis movement measurement is illustrated, and the laser distance 
measuring device for the Y-axis movement measurement is not shown. 
The optical axis of the laser distance measuring devices 5 is set at the 
same level as the wafer 3 surface, for avoiding Abbe's error. Denoted at 
13 is light projecting means for projecting light onto the wafer 3 
surface. Denoted at 14 is light receiving means for detecting incidence 
position information of reflected light from the wafer 3 surface. The 
light projecting means 13 and the light receiving means 14 are constituent 
elements of level measuring means for measuring the level (height) of the 
wafer 3 surface. 
For manufacture of semiconductor devices, the reticle 7 and the wafer 3 are 
positioned in a predetermined interrelationship and, thereafter, shutter 
means (not shown) is opened and closed such that the electronic circuit 
pattern on the reticle 7 surface is projected and printed on the wafer 3 
surface. Subsequently, by means of the wafer stage 2, the wafer 3 is moved 
by a predetermined amount along the X-Y plane such that the reticle 7 and 
the wafer 3 are positioned again. In this manner, the remaining zones 
(shot areas) of the wafer are exposed sequentially through projection 
exposure (step-and-repeat exposure process). After completion of exposures 
of all the zones of the wafer 3 surface, the wafer is processed by a 
developing treatment and so on which are known per se, and semiconductor 
devices are manufactured. 
How to measure coma of the projection optical system 6 of the projection 
exposure apparatus of FIG. 1, will be explained below. 
FIG. 3A illustrates a reticle mark 7a formed on a reticle 7, which mark 
comprises a pattern 1 (reference pattern) and a pattern 2. Areas with 
hatching depict light blocking areas. FIG. 3B shows a pattern image 
(resist pattern) of the reticle mark 7a, as formed on the wafer 3 surface 
through the projection optical system 6. The area with hatching depicts 
the resist pattern. For convenience, in FIG. 3B, only an image 31a of the 
outside periphery 31 of the pattern 1 of FIG. 3A and an image 33a of the 
inside periphery 33 of the pattern 2 of FIG. 3A are illustrated. 
In the present embodiment, first, the reticle pattern 7a shown in FIG. 3A 
is illuminated, and it is printed by projection exposure onto the resist 
coating of the wafer 3 (this is called "first printing"). At this moment, 
the surface of the resist of the wafer 3 is placed and held at the best 
image plane position of the projection optical system 6. Also, the movable 
stage 2 is moved stepwise along the X-Y plane, such that plural reticle 
patterns 7a are printed on the wafer through the "first printing". 
FIG. 4A shows resist patterns on a wafer formed through a developing 
process after the first printing. The resist patterns of FIG. 4A are those 
of the pattern 1 (reference pattern) only, of the patterns shown in FIG. 
3A. Reference characters "B.F" in FIG. 4A (and in FIG. 4B) represent "best 
focus". 
Subsequently, the reticle pattern 7a is printed by projection exposure on 
the wafer 3 again (this is called "second printing") while shifting the 
stage 2 by an amount corresponding to a distance S relative to the first 
printing, so that the center 34 of the pattern 2, of the patterns shown in 
FIG. 3A, is aligned with the resist pattern 31a (of the pattern 1) having 
been formed on the wafer 3. The second printing operation is performed 
while moving the Z stage to shift the wafer in the focusing direction 
through some steps, from the best imaging plane (defocus=0). 
FIG. 4B illustrates reticle patterns 7a as formed on the wafer 3 as a 
result of the first printing followed by a developing process and the 
second printing followed by a developing process, while sequentially 
changing the position in the focusing direction. 
Subsequently, a deviation .DELTA.d (image shift amount) between the center 
position as detected from the outside edge (outside periphery) 31a having 
been printed through the first printing and the center position as 
detected from the inside edge (inside periphery) 33a having been printed 
through the second printing, is measured. Such positional information of 
the resist patterns 31a and 33a is obtainable by using a commercially 
available registration measuring device such as KLA-5011 (trade name) 
available from KLA Co., LA-3000 (trade name) available from Hitachi Denshi 
Engineering Co., on METRA2100 (trade name) available from OSI Co. 
In this embodiment, from deviations .DELTA.d detected in this manner, a 
graph similar to that of FIG. 2 is prepared. From the thus prepared graph, 
those results corresponding to the coma of the projection optical system 6 
are provided. On the basis of those results as well as the graph of FIG. 
2, the amount of coma of the projection optical system 6 is discriminated 
(measured). 
FIGS. 5A and 5B show projection waveforms as detected by a registration 
measuring device in relation to the resist patterns 31a and 33a in this 
embodiment, as well as how the centers of the pattern images (outside 31a 
and inside 33a) are detected from the projection waveforms. In this 
example, a projection waveform is sliced with respect to a certain 
intensity, and the center of each pattern image is determined on the basis 
of the position of a mid-point of the sliced waveform. 
In the present invention, the measurement may be based on any other 
measurement process such as, for example, a template matching method 
wherein matching is performed with respect to a predetermined waveform, or 
a method wherein symmetry is measured for evaluation. Also, the results of 
measurements made in the X and Y directions may be integrated (vector 
combination) and, on that occasion, the direction and magnitude of coma 
can be discriminated. 
FIG. 6 is a schematic view of a main portion of a second embodiment of the 
present invention, wherein the coma detecting method of the present 
invention for detecting coma of a projection optical system is 
incorporated into a semiconductor device manufacturing projection exposure 
apparatus. This embodiment has features, as compared with the first 
embodiment of FIG. 1, that a slit 10 and a photoelectric sensor 11 are 
mounted on the stage 2, that a reticle mark (single pattern) 7a 
constituting a slit opening 7b such as illustrated in FIG. 7A is formed on 
the reticle 7 (here, components are so set that the slit opening 7b of the 
reticle mark 7a is to be projected by the projection optical system 6 in 
the same size as that of the slit opening 10b of the slit 10), and that 
the reticle mark 7a is projected by the projection optical system 6 upon 
the slit 10 surface. The remaining portion of this embodiment has 
substantially the same structure as that of the first embodiment. 
In this embodiment, the position of the stage 2 in the Z direction is so 
set that the position of the slit 10 in the focusing direction is placed 
at the best image plane position. Subsequently, the X-Y stage is moved so 
that the slit 10 moves across the projected image of the reticle mark of 
the reticle 7. 
After this, the stage 2 is moved in the Z direction and, while sequentially 
changing the position of the slit 10 in the focusing direction from the 
best image plane position, the stage scan is repeated sequentially. 
FIGS. 8A through 8E illustrate signals obtained through the photoelectric 
sensor 11 in relation to pattern images of the reticle mark 7a. The 
illustrated case is the relationship between the position of the X-Y stage 
and the light quantity as detectable at the photoelectric sensor 11, in 
cases wherein the amount of defocus in the focusing direction is changed 
sequentially. From the values .DELTA.d of the amount of image shift 
relative to the amount of defocus, thus obtained, the amount of coma of 
the projection optical system is determined essentially in the same manner 
as in the first embodiment. 
FIGS. 9A1 through 9B2 are schematic views, respectively, each showing a 
pattern on a reticle and each for explaining a third embodiment of the 
present invention for detecting coma of a projection optical system. 
In the example of FIGS. 9A1 and 9A2, reticle patterns each being similar to 
the reticle pattern 7a of FIG. 3A are formed and juxtaposed on the surface 
of a reticle. Upper patterns correspond to the pattern 1 of FIG. 3A, and 
lower patterns correspond to the pattern 2 of FIG. 3A. Of these patterns, 
particular patterns are defined with steps (level differences). Namely, 
these particular patterns are at defocused positions. With the provision 
of such defocused reticle patterns (patterns 2), similar pattern images as 
those of FIGS. 4A and 4B are obtained without moving the stage 2 in the 
focusing direction as in the first embodiment of FIG. 1. The manner of 
measuring coma of the projection optical system is substantially the same 
as that of the first embodiment. 
In the example of FIGS. 9B1 and 9B2, reticle patterns each being similar to 
the reticle pattern 7a of FIG. 7A are formed and juxtaposed on the surface 
of a reticle. Lower reticle patterns 7a.sub.2 of FIGS. 9B1 and 9B2 
correspond to the reference pattern. Upper reticle patterns 7a.sub.1 are 
formed with steps (level differences). Thus, the patterns 7a.sub.1 are at 
defocused positions. With the provision of such defocused reticle patterns 
7a.sub.1, signals related to pattern images similar to those of FIGS. 8A 
through 8E are obtained without moving the stage 2 in the focusing 
direction as in the second embodiment of FIG. 6. The manner of measuring 
coma of the projection optical system is substantially the same as that of 
the first embodiment. 
FIGS. 10-12 are schematic views of embodiments of the present invention, 
wherein the invention is applied to a projection exposure apparatus which 
is provided with means for measuring coma of a projection optical system 
and means for correcting coma. Like numerals as those of FIG. 6 are 
assigned to corresponding elements. 
FIG. 10 shows an embodiment wherein one or more of the lens elements of the 
projection optical system is able to be tilted with respect to or 
translated off the optical axis of the projection optical system, for 
correcting coma. 
FIG. 11 shows an embodiment wherein a parallel flat plate 16 is provided 
between the projection optical system 6 and the reticle 7 (object plane), 
which parallel flat plate is able to be tilted with respect to the optical 
axis of the projection optical system, for correcting coma. 
FIG. 12 shows an embodiment wherein a parallel flat plate 17 is provided 
between the projection optical system 6 and the wafer 3 (image plane), 
which parallel flat plate is able to be tilted with respect to the optical 
axis of the projection optical system, for correcting coma. 
In the embodiments of FIGS. 10-12, the relation between the amount of coma 
of the projection optical system and the amount of tilt or translation to 
or off the optical axis is determined beforehand on the basis of 
simulations or experiments. In accordance with the magnitude and direction 
of coma of the projection optical system as can be determined with the 
coma measuring method having been described, correction of coma is 
performed. It is to be noted that the embodiments of FIGS. 10-12 may be 
arranged to perform coma measurement in accordance with the method 
described with reference to the first embodiment. 
The embodiments described above may be modified. Examples are: the object 
plane and the image plane may be reversed (the state of defocus at the 
wafer side is replaced by a similar state at the reticle side); the first 
best focus and the second defocus in the first embodiment may be replaced 
by first defocus and second best focus; in the second and third 
embodiments, the measurement may be made with respect to both of the X and 
Y directions to specify the direction and magnitude of coma of the 
projection lens system; the measurement mark (reticle mark) may be 
provided by a number of marks for enhancement of measurement precision; in 
place of receiving pattern images for detection of coma at different 
defocused positions, the amount of coma may be determined by receiving the 
image at a single defocused position and by using the graph of FIG. 2. 
Next, an embodiment of a device manufacturing method according to the 
present invention which uses one of the projection exposure apparatuses 
described above, will be explained. 
FIG. 13 is a flow chart of the sequence of manufacturing a semiconductor 
device such as a semiconductor chip (e.g., an IC or an LSI), a liquid 
crystal panel or a CCD, for example. Step 1 is a design process for 
designing the circuit of a semiconductor device. Step 2 is a process for 
manufacturing a mask on the basis of the circuit pattern design. Step 3 is 
a process for manufacturing a wafer by using a material such as silicon. 
Step 4 is a wafer process which is called a pre-process wherein, by using 
the so prepared mask and wafer, circuits are practically formed on the 
wafer through lithography. Step 5 subsequent to this is an assembling step 
which is called a post-process wherein the wafer processed by step 4 is 
formed into semiconductor chips. This step includes assembling (dicing and 
bonding) and packaging (chip sealing). Step 6 is an inspection step 
wherein an operability check, durability check a and so on of the 
semiconductor devices produced by step 5 are carried out. With these 
processes, semiconductor devices are finished and they are shipped (step 
7). 
FIG. 14 is a flow chart showing details of the wafer process. Step 11 is an 
oxidation process for oxidizing the surface of a wafer. Step 12 is a CVD 
process for forming an insulating film on the wafer surface. Step 13 is an 
electrode forming process for forming electrodes on the wafer by vapor 
deposition. Step 14 is an ion implanting process for implanting ions to 
the wafer. Step 15 is a resist process for applying a resist 
(photosensitive material) to the wafer. Step 16 is an exposure process for 
printing, by exposure, the circuit pattern of the mask on the wafer 
through the exposure apparatus described above. Step 17 is a developing 
process for developing the exposed wafer. Step 18 is an etching process 
for removing portions other than the developed resist image. Step 19 is a 
resist separation process for separating the resist material remaining on 
the wafer after being subjected to the etching process. By repeating these 
processes, circuit patterns are superposedly formed on the wafer. 
While the invention has been described with reference to the structures 
disclosed herein, it is not confined to the details set forth and this 
application is intended to cover such modifications or changes as may come 
within the purposes of the improvements or the scope of the following 
claims.