U.S. patent application number 09/848422 was filed with the patent office on 2001-10-18 for method of inspecting pattern and apparatus thereof.
Invention is credited to Doi, Hideaki, Hiroi, Takashi, Kuni, Asahiro, Maeda, Shunji, Ninomiya, Takanori, Nozoe, Mari, Shinoda, Hiroyuki, Shishido, Chie, Sugimoto, Aritoshi, Takafuji, Atsuko, Tanaka, Maki, Usami, Yasutsugu, Watanabe, Masahiro, Yoda, Haruo.
Application Number | 20010030300 09/848422 |
Document ID | / |
Family ID | 15058486 |
Filed Date | 2001-10-18 |
United States Patent
Application |
20010030300 |
Kind Code |
A1 |
Shishido, Chie ; et
al. |
October 18, 2001 |
Method of inspecting pattern and apparatus thereof
Abstract
A method for inspecting a pattern formed on a substrate,
includes the steps of moving a table along a first direction on
which a substrate to be inspected is mounted, irradiating a
converged electron beam on the substrate by scanning the converged
electron beam along a second direction which is perpendicular to
the first direction; detecting an electron radiated from the
substrate by the irradiation of the converged electron beam in
which the movement of the table and the scanning of the converged
electron beam are synchronized; forming a digital image of the
substrate from the detected electron; improving a quality of the
digital image by filtering the compensated digital image; and
detecting a defect of a pattern formed on the substrate by using
the improved quality digital image.
Inventors: |
Shishido, Chie;
(Yokohama-shi, JP) ; Hiroi, Takashi;
(Yokohama-shi, JP) ; Yoda, Haruo; (Nishitama-gun,
JP) ; Watanabe, Masahiro; (Yokohama-shi, JP) ;
Kuni, Asahiro; (Setagaya-ku, JP) ; Tanaka, Maki;
(Yokohama-shi, JP) ; Ninomiya, Takanori;
(Hiratsuka-shi, JP) ; Doi, Hideaki; (Oota-ku,
JP) ; Maeda, Shunji; (Yokohama-shi, JP) ;
Nozoe, Mari; (Oume-shi, JP) ; Shinoda, Hiroyuki;
(Choufu-shi, JP) ; Takafuji, Atsuko; (Nerima-ku,
JP) ; Sugimoto, Aritoshi; (Bunkyou-ku, JP) ;
Usami, Yasutsugu; (Hitachinaka-shi, JP) |
Correspondence
Address: |
ANTONELLI TERRY STOUT AND KRAUS
SUITE 1800
1300 NORTH SEVENTEENTH STREET
ARLINGTON
VA
22209
|
Family ID: |
15058486 |
Appl. No.: |
09/848422 |
Filed: |
May 4, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09848422 |
May 4, 2001 |
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09610954 |
Jul 6, 2000 |
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6236057 |
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09610954 |
Jul 6, 2000 |
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09081636 |
May 20, 1998 |
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6087673 |
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Current U.S.
Class: |
250/559.44 |
Current CPC
Class: |
G01N 21/95607
20130101 |
Class at
Publication: |
250/559.44 |
International
Class: |
G01N 021/86 |
Foreign Application Data
Date |
Code |
Application Number |
May 21, 1997 |
JP |
9-131460 |
Claims
What is claimed is:
1. A method for inspecting a pattern formed on a substrate,
comprising the steps of: moving a table along a first direction on
which a substrate to be inspected is mounted; irradiating a
converged electron beam on the substrate by scanning the converged
electron beam along a second direction which is perpendicular to
the first direction; detecting an electron radiated from the
substrate by the irradiation of the converged electron beam in
which the movement of the table and the scanning of the converged
electron beam is synchronized; forming a digital image of the
substrate from the detected electron; improving a quality of the
digital image by filtering the compensated digital image; and
detecting a defect of a pattern formed on the substrate by using
the improved quality digital image.
2. A method according to claim 1, further comprising the steps of:
optically detecting a height of the table; and controlling a focus
of the converged electron beam to focus onto the substrate.
3. A method according to claim 1, wherein the step of detecting a
defect includes comparing a first improved quality digital image
with a second improved quality digital image which are essentially
the same image.
4. A method for inspecting a pattern formed on a substrate,
comprising the steps of: irradiating a converged electron beam on
the substrate by scanning the converged electron beam; obtaining a
digital image of the substrate by detecting an electron radiated
from the substrate by the irradiation of the converged electron
beam; compensating at least one of a brightness and shading of the
digital image; detecting a candidate defect by comparing
compensated digital images with one another; and detecting a true
defect among the candidate defect.
5. A method according to claim 4, wherein true defect candidate is
detected by aligning the compensated digital images which are
essentially the same image with one another.
6. A method according to claim 4, wherein the true defect is
detected by using an information of coordinate data of the
candidate defect.
7. A method according to claim 4, wherein a distortion of the
digital image is also compensated in the compensating step.
8. A method for inspecting a pattern formed on a substrate,
comprising the steps of: irradiating a converged electron beam on
the substrate by scanning the converged electron beam; obtaining a
digital image of the substrate by detecting an electron radiated
from the substrate by the irradiation of the converged electron
beam; compensating at least a brightness of the digital image;
improving a quality of the digital image by filtering the
compensated digital image; detecting a candidate defect from the
compensated digital images; and outputting an information regarding
to a true defect among the detected candidate defect.
9. A method according to claim 8, wherein the candidate defect is
detected by comparing the compensated digital image with another
compensated digital image which are essentially the same image.
10. A method according to claim 8, wherein the information of the
true defect is obtained from a coordinate data of the candidate
defect.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] This is a continuation of U.S. application Ser. No.
09/610,954, filed Jul. 6, 2000, which is a continuation of U.S.
application Ser. No. 09/081,636, filed May 20, 1998 (now U.S. Pat.
No. 6,087,673), the subject matter of which is incorporated by
reference herein.
BACKGROUND OF THE INVENTION
[0002] The present invention relates to a method of inspecting a
pattern and an apparatus thereof, in which a defect or a candidate
for a defect is inspected by obtaining an image indicating physical
properties of objects such as a semiconductor wafer, a TFT, and a
photo mask with the use of an electron beam or a light beam, and by
then comparing the image with an image obtained differently. More
particularly, the present invention relates to a method of
inspecting a pattern and an apparatus thereof, in which a
microscopic defect or a candidate for a microscopic defect is
inspected.
[0003] Concerning an inspection for recognizing a defect of a
pattern, known as a prior art technology 1, as disclosed in
Japanese Laid-Open Patent Publication No. 57-196377, is as follows.
First, a pattern of an object to be inspected, such as a
semiconductor including a pattern with a repetition, is detected,
and the pattern detected is stored. Then, position alignment is
performed in a pixel or picture element unit between the detected
pattern and a pattern stored in advance. Finally, a defect is
recognized by extracting a mismatch between the two patterns over
which the position alignment has been made. Also, known as a prior
art technology 2, as disclosed in Japanese Laid-Open Patent
Publication No. 3-177040, is a technique which makes it possible to
improve, of a problem of a mismatch between the both images in a
normal part, a portion of the problem that is attributed to a
missing of a position at which the both images are to be detected.
Namely, described in the prior art technology 2 is the following
technique. First, a pattern of an object is detected as an image
signal. Then, position alignment is performed in a pixel unit
between the image signal of the detected pattern and an image
signal of the pattern stored in advance or an image signal of the
pattern detected differently. Still then, with one pixel or less of
accuracy, additional position alignment is further made between the
image signals over which the position alignment has been made in
the pixel unit. Finally, a defect of the pattern is recognized by
extracting and comparing errors of the image signals of the two
patterns over which the additional position alignment has been made
with one pixel or less of accuracy.
[0004] Between the two images to be compared, even in the normal
part, there exists differences such as an infinitesimal difference
in pattern configuration, a difference in a gradation or tone
value, a distortion of the pattern, and a shift of the position,
which are attributed to the object to be inspected and an image
detecting system. Namely, the mismatch in the normal part is
classified into a mismatch due to the object to be inspected and a
mismatch due to the image detecting system. The mismatch due to the
object to be inspected is caused by a subtle difference in
repetition patterns produced through a wafer manufacturing process
such as an exposure, a developing and an etching. This, on the
detected images, appears as the infinitesimal difference in pattern
configuration and the difference in the gradation value. The
mismatch due to the image detecting system is caused by variations
in illuminating light quantity, an oscillation of a stage, a
variety of electrical noises, and a missing of the position at
which the both images are to be detected. These, on the detected
images, appear as a difference in a gradation value of partial
images, the distortion of the pattern, and the position shift of
the images.
[0005] In the above-mentioned prior art technology 1, there existed
the following problem. Since the above-described factors cause the
mismatch to occur even in the normal part, if every mismatched
portion is judged to be a defect, it turns out that there occurs a
lot of false information. If, in order to prevent this, a criterion
for the defect judgement is lowered, it becomes impossible to
detect a microscopic defect.
[0006] Also, in the above-mentioned prior art technology 2, of the
infinitesimal difference in the pattern configuration, the
difference in the gradation value, the distortion of the pattern,
and the position shift, which are attributed to the object to be
inspected and the image detecting system, there existed an effect
of reducing an influence of the position shift between the images.
The other differences, however, were not taken into
consideration.
SUMMARY OF THE INVENTION
[0007] It is an object of the present invention to provide, in
order to solve the above-mentioned problems accompanied by the
prior arts, a method of inspecting a pattern and an apparatus
thereof, which make it possible to further reduce the number of
false information caused by a mismatch due to an object to be
inspected and an image detecting system, and to detect a more
microscopic defect or a candidate for a more microscopic
defect.
[0008] It is another object of the present invention to provide,
when a pattern formed on an object to be inspected is inspected by
means of an electron microscope, a method of inspecting the pattern
and an apparatus thereof, which make it possible to further reduce
the number of false information caused by a mismatch due to the
object to be inspected and an image detecting system, and to detect
a more microscopic defect or a candidate for a more microscopic
defect.
[0009] It is still another object of the present invention to
provide a method of inspecting a pattern and an apparatus thereof,
which make it possible to obtain an image signal having a stable
gradation value (a value of light and shade) from an inspection
through an electron microscope of a pattern formed on an object to
be inspected, and to stably detect a more microscopic defect or a
candidate for a more microscopic defect.
[0010] In order to attain the above-described object, the present
invention is characterized by the configuration described below,
when a defect or a candidate for a defect of an object to be
inspected is detected by comparing a first two-dimensional image,
on each pixel of which a gradation value is a sampling value of a
physical quantity at each point in one area to be inspected on the
object to be inspected, with a second two-dimensional image, on
each pixel of which a gradation value is a sampling value at each
point in the other area which is supposed to have the same physical
quantity as the abovementioned physical quantity.
[0011] Namely, the present invention is characterized by comprising
the steps of performing position alignment between the first
two-dimensional image and the second two-dimensional image in a
pixel unit, calculating one pixel or less of position shift
quantity of corresponding portions between the first
two-dimensional image f1(x, y) and the second two-dimensional image
g1(x, y) over which the position alignment has been made in the
pixel unit, determining for each pixel sub(x, y), i.e. distance
(difference) between a partial image (an image in a smaller area)
in the first two-dimensional image and a partial image (an image in
a smaller area) in the second two-dimensional image which have the
one pixel or less of position shift quantity, determining for each
pixel an allowable range (threshold values thH(x, y) and thL(x, y)
at an upper limit and a lower limit, respectively) of the distance
(difference) from the one pixel or less of position shift quantity
determined and gradation values of the first two-dimensional image
and the second two-dimensional image, checking whether or not the
above-described distance (difference) between the partial images
falls within the above-described allowable range for each pixel,
and judging a pixel, on which the distance between the partial
images is within the allowable range, to be an non-defective
candidate and a pixel, on which the distance between the partial
images is beyond the allowable range, to be a defective
candidate.
[0012] Also, the present invention is characterized by comprising
the steps of performing position alignment between the first
two-dimensional image and the second two-dimensional image in a
pixel unit, calculating one pixel or less of position shift
quantity of corresponding portions between the first
two-dimensional image and the second two-dimensional image over
which the position alignment has been made in the abovementioned
pixel unit, determining a distance (difference) between the first
two-dimensional image and the second two-dimensional image in each
of a plurality of states in which the position relationship between
the first two-dimensional image and the second two-dimensional
image is shifted in a variety of directions by predetermined
quantities determined by .alpha., .beta. from a state in which the
above-stated one pixel or less of position shift quantity has been
amended, comparing with each other a distance (difference) between
partial images in the both two-dimensional images determined for
each of the above-mentioned position relationships in the plurality
of states and determining for each pixel a maximum and a minimum of
the distances between the partial images, determining for each
pixel an allowable value (threshold values at an upper limit and a
lower limit) of the distances between the partial images from a
gradation value of the first two-dimensional image and that of the
second two-dimensional image over which the position alignment has
been made in the pixel unit, comparing a value obtained by adding
the allowable value to the maximum with a value obtained by
subtracting the allowable value from the minimum, and judging a
pixel, on which the signs of them are opposite (the polarity is
different), to be an non-defective candidate and a pixel, on which
the signs of them are same (the polarity is same), to be a
defective candidate.
[0013] Besides, the present invention provides a method and an
apparatus for inspecting a defect or a candidate for a defect of an
object to be inspected, by comparing a first two-dimensional image,
on each pixel of which detected as a gradation value is a sampling
value of a physical quantity at each point on the object to be
inspected, with a second two-dimensional image on each pixel of
which represented as a gradation value is a sampling value.
Incidentally, in this invention, the second two-dimensional image
is employed as an object compared with the first two-dimensional
image. In addition, the present invention is characterized in that
an allowable range is calculated in correspondence with a position
shift quantity between an image in a predetermined area in the
first two-dimensional image and an image in a predetermined area in
the second two-dimensional image, a distance or a difference
between the above-mentioned first two-dimensional image and the
above-mentioned second two-dimensional image is determined using
the gradation values, and a pixel is judged to be the defect or the
candidate for the defect depending on whether or not the distance
or the difference determined using the gradation values is within
the calculated allowable range described above.
[0014] In addition, in the above-described method of inspecting a
pattern and the apparatus thereof, the present invention is
characterized by calculating a local change rate of a gradation
value, using any one of the following formulas 14-1, 14-2, and
14-3, or enlarging the formulas 14-1, 14-2, and 14-3 up to n*n
pixel in proximity to a pixel to which attention is being given.
Assuming that f (x, y) is a gradation value of the pixel to which
attention is being paid, and d x(x, y) and d y(x, y) are local
change rates of the gradation value in a x-direction and a
y-direction, respectively, the formulas to be used are as
follows.
dx(x,y)=f(x+1,y)-f(x,y)
dy(x,y)=f(x,y+1)-f(x,y) 14-1
dx(x,y)=[{f(x+1,y)+f(x+1,y+1)}-{f(x,y)+f(x,y+1)}]/2
dy(x,y)=[{f(x,y+1)+f(x+1,y+1)}-{f(x,y)+f(x+1,y)}]/2 14-2
dx(x,y)=dy(x,y)=max{f(x,y), f(x+1,y), f(x,y+1),
f(x+1,y+1}-min{f(x,y), f(x+1,y), f(x,y+1), f(x+1,y+1)} 14-3
[0015] Moreover, in the above-described method of inspecting a
pattern and the apparatus thereof, the present invention provides a
method of calculating a variation allowable range of the gradation
value, which is to be determined as a function of the local change
rate of the gradation value, with the use of either of the
following formulas 15-1, 15-2.
[0016] an upper limit in a variation allowable range of a gradation
value at a coordinate
(x,y)=.vertline.dx(x,y)*.alpha..vertline.+.vertline.dy(x,y)*.beta..vertlin-
e.
[0017] a lower limit in a variation allowable range of a gradation
value at a coordinate
(x,y)=-.vertline.dx(x,y)*.alpha..vertline.-.vertline.dy(x,y)*.beta..vertli-
ne. 15-1
[0018] an upper limit in a variation allowable range of a gradation
value at a coordinate
(x,y)={square root}{square root over (
)}{(dx(x,y)*.alpha.).sup.2+(dy(x,y)- *.beta.).sup.2}
[0019] a lower limit in a variation allowable range of a gradation
value at a coordinate
(x,y)=-{square root}{square root over (
)}{(dx(x,y)*.alpha.).sup.2+(dy(x,y- )*.beta.).sup.2} 15-2
[0020] assuming that dx(x,y) and dy(x,y) are the local change rates
of the gradation value in a x-direction and a y-direction,
respectively, which are calculated from gradation values of a
plurality of pixels in proximity to the pixel to which attention is
being paid, and .alpha., .beta. are real numbers greater than
zero.
[0021] Furthermore, in the above-described method of inspecting a
pattern and the apparatus thereof, the present invention provides a
method of treating, in such a manner as to be described in any one
of the following methods 16-1, 16-2, and 16-3, the variation
allowable range of the gradation value which is to be determined as
a function of a representative gradation value.
[0022] 16-1 Employed as the representative gradation value is a
maximum of the gradation value within a range of .rho.*.rho. pixel
in proximity to a pixel (x, y) to which attention is being given,
and the variation allowable range is determined as a function of
the representative gradation value.
[0023] 16-2 Employed as the representative gradation value is an
average value of the gradation value within a range of .rho.*.rho.
pixel in proximity to a pixel (x, y) to which attention is being
given, and the variation allowable range is determined as a
function of the representative gradation value.
[0024] 16-3 A look-up table for the representative gradation value
is prepared beforehand, and, in accordance therewith, the variation
allowable range is determined.
[0025] Further, in the above-described method of inspecting a
pattern and the apparatus thereof, the present invention is
characterized in that a method of superposing values obtained by a
plurality of methods out of the above-described methods (1), (2),
and (3) is as follows. Summing up a plurality of values obtained by
a plurality of methods out of the methods (1), (2), and (3), taking
the square root of summation of squares of a plurality of values
out of the methods (1), (2), and (3), or taking the square root of
summation of a square of summation of a plurality of values out of
the methods (1), (2), and (3), and a square of summation of the
other plurality of values.
[0026] Still further, in the above-described method of inspecting a
pattern and the apparatus thereof, the present invention is
characterized by performing part of the whole process or the whole
process with a plurality of pixels as one pixel.
[0027] Even further, in the above-described method of inspecting a
pattern and the apparatus thereof, the present invention is
characterized by embodying content described with a plurality of
pixels as one pixel.
BRIEF DESCRIPTION OF THE DRAWINGS
[0028] FIG. 1 is a schematic configuration diagram showing a first
embodiment of a method of inspecting a pattern and an apparatus
thereof in which an electron microscope in connection with the
present invention is employed;
[0029] FIG. 2 is a layout diagram of a semiconductor wafer shown as
an example of an object to be inspected in connection with the
present invention;
[0030] FIG. 3 is a diagram for explaining a sampling error in
connection with the present invention;
[0031] FIG. 4 is a schematic configuration diagram showing a first
embodiment of a method of inspecting a pattern and an apparatus
thereof in which an optical microscope in connection with the
present invention is employed;
[0032] FIG. 5 is a diagram showing a concrete configuration of a
threshold arithmetic circuit in connection with the first
embodiment of the present invention;
[0033] FIG. 6 is a diagram for explaining a first modification in
the first embodiment shown in FIG. 1;
[0034] FIG. 7 is a diagram for explaining a second modification in
the first embodiment shown in FIG. 1;
[0035] FIG. 8 is a schematic configuration diagram showing a second
embodiment of a method of inspecting a pattern and an apparatus
thereof in which an electron microscope according to the present
invention is employed;
[0036] FIG. 9(a), (b), and (c) are diagrams for explaining a
meaning of generation of a position-shifted image in connection
with the second embodiment of the present invention;
[0037] FIG. 10(a), (b), and (c) are diagrams for explaining a
meaning of generation of a position-shifted image, as is the case
with the FIG. 9(a), (b), and (c);
[0038] FIG. 11 is a schematic configuration diagram showing an
embodiment of an electron microscope in connection with the present
invention;
[0039] FIG. 12 is a diagram showing a concrete configuration of a
preprocessing circuit in connection with the present invention;
and
[0040] FIG. 13 is a diagram for explaining content to be amended by
the preprocessing circuit shown in FIG. 12.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0041] Described below, using the accompanying drawings, are
embodiments of a method of inspecting a pattern and an apparatus
thereof in connection with the present invention.
[0042] First Embodiment
[0043] Shown in FIG. 1 is a first embodiment of a method of
inspecting a pattern and an apparatus thereof in connection with
the present invention. Here, irradiation of an electron beam 30
scans an object to be inspected 100 such as a wafer, thus detecting
electrons produced from the object to be inspected 100. Then, based
on variations in the intensity, an electron beam image of the
scanned part is obtained so as to perform a patter inspection using
the electron beam image.
[0044] Employed as the object to be inspected 100 is, for example,
a semiconductor wafer 1 as shown in FIG. 2. Arranged on the
semiconductor wafer 1 are a great umber of chips 1a, which finally
turn out to become an identical product to each other. As is shown
in an enlarged view of the Figure, pattern layout within a chip 1a
comprises a memory mat unit 1c, on which memory cells are regularly
arranged two-dimensionally at an identical pitch, and a peripheral
circuit unit 1b. When applied to an inspection of a pattern in the
semiconductor wafer 1, a defect is recognized by first storing a
detection image on a chip (for example, a chip 1d) and then
comparing it with a detection image on another chip (for example, a
chip 1e) (hereinafter, referred to as "chip comparison"), or by
first storing a detection image in a memory cell (for example, a
memory cell 1f) and then comparing it with a detection image in
another memory cell (for example, a memory cell 1g) (hereinafter,
referred to as "cell comparison").
[0045] If repetition patterns on the object to be inspected 100
(taking the semiconductor wafer as an example, chips among
themselves or cells among themselves) were strictly identical to
each other and the same detection images were able to be obtained,
recognition of a defect would be possible since only the defect
mismatches when the images are compared with each other.
[0046] Actually, however, there does exist a mismatch between the
both images even in a normal part. The mismatch in the normal part
is classified into a mismatch due to an object to be inspected and
a mismatch due to an image detecting system. The mismatch due to
the object to be inspected is caused by a subtle difference in
repetition patterns produced through a wafer manufacturing process
such as an exposure, a developing and an etching. This, on the
detected images, appears as an infinitesimal difference in the
pattern configuration and a difference in a gradation value. The
mismatch due to the image detecting system is caused by variations
in illuminating light quantity, an oscillation of a stage, a
variety of electrical noises, and a missing of the position at
which the both images are to be detected. These, on the detected
images, appear as a difference in a gradation value of partial
images, distortion of the pattern, and position shift of the
images.
[0047] In the first embodiment in connection with the present
invention, a defect judgment is made in the following manner.
First, a detection image (a first two-dimensional image), over
which position alignment has been made in a pixel unit and the
gradation value of which is f1(x,y) at a coordinate (x,y), is
compared with a detection image (a second two-dimensional image),
over which position alignment has been made in a pixel unit and the
gradation value of which is g1(x,y) at a coordinate (x,y). Then,
threshold values (allowable values), which are used at the time of
judging a defect, are set for each pixel by considering a result of
the comparison and such factors as position shift of the pattern
and a difference in the gradation values. Finally, based on the
threshold values (allowable values) set for each pixel, the defect
judgment is made.
[0048] The present pattern inspecting system, as shown in FIG. 1
and FIG. 11, comprises a detecting unit 101, an image fetching unit
102, an image processing unit 103, and a general control unit 104
for controlling the whole system. Additionally, the present pattern
inspecting system further comprises an inspection room 105 the
inside of which is exhausted into a vacuum and a preliminary room
(not illustrated) through which the object to be inspected 100 is
transported into or out of the inspection room 105. The preliminary
room is configured to be exhausted into a vacuum independently of
the inspection room 105.
[0049] First, the description will be given below concerning the
detecting unit 101, using FIG. 1 and FIG. 11. The inspection room
105 in the detecting unit 101 mainly comprises an electronic
optical system 106, an electron detecting unit 107, a sample room
109, and an optical microscope unit 108. The electronic optical
system 106 comprises an electron gun 31, an electron beam
extraction electrode 111, a condenser lens 32, a blanking deflector
113, a scanning deflector 34, a diaphragm 114, an objective lens
33, a reflector 117, an EXB deflector 115, and a Faraday cup (not
illustrated) for detecting a beam electric current. The reflector
117 is made conical in shape so as to have an effect of
multiplexing secondary electrons.
[0050] Of units furnished in the electron detecting unit 107, for
example, an electron detector 35, which detects electrons such as
secondary electrons and reflected electrons, is provided above, for
example, the objective lens 33 within the inspection room 105. An
output signal of the electron detector 35 is amplified by an
amplifier 36 provided outside the inspection room 105.
[0051] The sample room 109 comprises a sample stand 130, a X stage
131, a Y stage 132, a position monitoring range finder 134, and an
inspected substrate height finder 135. Incidentally, the stages may
be provided with a rotating stage.
[0052] The position monitoring range finder 134 monitors positions
of units such as the stages 131 and 132, then transferring the
result to the general control unit 104. Also, the general control
unit 104 controls driving systems of the stages 131 and 132. This
eventually makes it possible for the general control unit 104 to
accurately grasp an area or a position onto which the electron beam
30 is irradiated based on these data.
[0053] The inspected substrate height finder 135 measures height of
the object to be inspected 100 placed on the stages 131 and 132,
using an optical measuring apparatus. Based on measurement data
measured by the inspected substrate height finder 135, a focal
length of the objective lens 33 for narrowing the electron beam 30
is dynamically amended so that the electron beam can be irradiated
under a condition that the focus is always achieved on an area to
be inspected. Incidentally, although, in FIG. 11, the height finder
135 is provided inside the inspection room 105, it is allowable
that the height finder 135 is provided outside the inspection room
105 so as to introduce light into the inside of the inspection room
105 through the glass windows.
[0054] The optical microscope unit 108 and the electronic optical
system 106 inside the inspection room 105 are in proximity to each
other, and at the same time are located apart to such an extent
that the both exerts no influence on each other. Naturally, the
distance between the electronic optical system 106 and the optical
microscope unit 108 is configured to be a known value. Moreover,
the X stage 131 or the Y stage 132 is configured to perform a
reciprocating movement along the known distance between the
electronic optical system 106 and the optical microscope unit 108.
The optical microscope unit 108 comprises a light source 142, an
optical lens 141, and a CCD camera 140. The optical microscope unit
108 detects an optical image of a circuit pattern formed on the
object to be inspected, for example, the semiconductor wafer 1, and
calculates rotation shift quantity of the circuit pattern based on
the optical image detected, thus transmitting the rotation shift
quantity calculated to the general control unit 104. This allows
the general control unit 104 to amend the rotation shift quantity
by, for example, rotating the rotation stage. Also, the general
control unit 104 transfers the rotation shift quantity to an
amendment control circuit 143. The amendment control circuit 143,
based on the rotation shift quantity, amends, for example, a
scanning deflection position of the electron beam caused by the
scanning deflector 34, thus making it possible to amend the
rotation shift. Also, the optical microscope unit 108 detects an
optical image of a circuit pattern formed on the object to be
inspected, for example, the semiconductor wafer 1, and observes the
optical image by, for example, displaying it on a monitor 150.
Then, the optical microscope unit 108, based on the optical image
observed and using an inputting means, inputs coordinates of an
inspected area into the general control unit 104, thereby making it
possible to set the inspected area towards the general control unit
104. It also become possible to measure in advance a pitch between
chips in the circuit pattern formed on, for example, the
semiconductor wafer 1 or a repetition pitch in repetition patterns
such as memory cells, and to input it into the general control unit
104. Incidentally, although, in FIG. 11, the optical microscope
unit 108 is provided inside the inspection room 105, it is
allowable that the optical microscope unit 108 is provided outside
the inspection room 105 so as to detect the optical image of the
semiconductor wafer 1 through the glass windows.
[0055] As shown in FIG. 1 and FIG. 11, the electron beam launched
from the electron gun 31, through the condenser lens 32 and the
objective lens 33, is narrowed into a beam diameter about a pixel
size on a sample surface. At this time, a ground electrode 38 and a
retarding electrode 37 apply a negative electric potential to the
sample so as to decrease speed of the electron beam between the
objective lens 33 and the object to be inspected (the sample) 100,
thus aiming at making the resolving power even higher in the
low-accelerating voltage region. When irradiated with the electron
beam, the object to be inspected (the wafer 1) 100 generates
electrons. A two-dimensional electron beam image of the object to
be inspected is obtained by a repetition scanning of the electron
beam in a X-direction by means of the scanning deflector 34 and by
detecting the electrons generated from the object to be inspected
100 in synchronization with a continuous movement of the object to
be inspected (the sample) 100 in a Y-direction by means of a stage
2. The electrons generated from the object to be inspected are
captured by the detector 35, and amplified by the amplifier 36. At
that time, in order to make a high rate inspection possible, it is
desirable to employ an electrostatic deflector with a high
deflecting speed as the scanning deflector 34 which performs the
repetition scanning of the electron beam in a X-direction, to
employ a thermal electric field radiation type electron gun, which
can shorten an irradiation time because it can increase the
electron beam current, and to employ, as the detector 35, a
semiconductor detector which allows a high rate driving.
[0056] Described next, using FIG. 1, FIG. 11, and FIG. 12, is the
image fetching unit 102. An electron detection signal detected by
the electron detector 35 in the electron detecting unit 107 is
amplified by the amplifier 36 and converted into digital image data
(gradation image data) by an A/D converter 39. An output of the A/D
converter 39 is configured to be transmitted by a light converting
means (light emitting device) 123, a transmitting means (optical
fiber cable) 124, and an electricity converting means (light
receiving device) 125. According to this configuration, it is
sufficient for the transmitting means 124 to have the same
transmitting rate as that of clock frequency in the A/D converter
39. The output of the A/D converter 39 is converted into an optical
digital signal by the light converting means (light emitting
device) 123, transmitted through optical transmission by the
transmitting means (optical fiber cable) 124, and converted into
the digital image data (gradation image data) by the electricity
converting means (light receiving device) 125. Namely, the
transmission is carried out in such a manner as to be converted
into a light signal. The reason is that, in order to guide
electrons 52 from the reflector 117 into the semiconductor detector
35, it is required to perform a floating of configuration
components from the semiconductor detector 35 to the light
converting means 123 (the semiconductor detector 35, the amplifier
36, the A/D converter 39, and the light converting means (light
emitting device) 123) up to a positive high electric potential by
means of a high voltage power supply (not illustrated). Strictly
speaking, it is sufficient to raise only the semiconductor detector
35 up to the positive high electric potential. It is desirable,
however, that the amplifier 36 and the A/D converter 39 are located
close to the semiconductor detector 35 in order to prevent a
mixture of noises and a deterioration of signals. Accordingly, it
is difficult to keep only the semiconductor detector 35 raised up
to the positive high electric potential, and in the end, the
above-mentioned configuration components as a whole are raised up
to the high electric potential. Namely, since the transmitting
means (optical fiber cable) 124 is formed with a high insulating
material, the image signal which was at the positive high electric
potential level at the light converting means (light emitting
device) 123, after having passed through the transmitting means
(optical fiber cable) 124, falls at an earth level, thus making it
possible to obtain output of an image signal at the earth level
from the electricity converting means (light receiving device)
125.
[0057] A preprocessing circuit (image amendment circuit) 40
comprises a dark level amending circuit 72, an electron source
fluctuation amending circuit 73, a shading amending circuit 74, and
so on. Digital image data (gradation image data) 71 obtained by the
electricity converting means (light receiving device) 125 undergo,
in the preprocessing circuit (image amendment circuit) 40, image
amendments such as a dark level amendment, an electron source
fluctuation amendment, and a shading amendment. The dark level
amendment in the dark level amending circuit 72, as shown in FIG.
13, amends a dark level with reference to a detection signal 71 in
a beam-blanking period, which is extracted based on a scanning line
synchronization signal 75 obtained from the general control unit
104. Namely, the reference signal for amending the dark level is
updated for each line, regarding as the dark level an average of
gradation values with, for example, a specific number of pixels at
a specific position during the beam-blanking period. In this way,
in the dark level amending circuit 72, the dark level amendment is
carried out by employing the detection signal, which is detected
during the beam-blanking period, as a reference signal to be
updated for each line. The electron source fluctuation amendment in
the electron source fluctuation amending circuit 73 is performed,
as is shown in FIG. 13, by normalizing a detection signal 76, to
which the dark level amendment has been made, with the use of a
beam electric current 77 monitored by the Faraday cup (not
illustrated) for detecting the above-described beam current with an
amendment period (for example, 100 kHz of line unit). Since there
is no rapid variation in the electron source fluctuation, it is
allowable to use a beam current which was detected one to several
lines before. As is shown in FIG. 13, the shading amendment in the
shading circuit 74 amends, for a detection signal 78 to which the
electron source fluctuation amendment has been made, variations in
light quantity due to a beam scanning position 79 obtained from the
general control unit 104. Namely, the shading amendment performs
the amendment (normalization) for each pixel, based on reference
illumination data 83 detected in advance. The shading amending
reference data 83 are created as follows. Image data detected in
advance are once stored in an image memory (for example, a unit
147), and then the image data stored are sent to a computer
provided in the general control unit 104 or a host computer
connected with the general control unit 104 over a network. The
computer provided in the general control unit 104 or the host
computer connected with the general control unit 104 over the
network processes the sent image data with software, thus creating
the shading amending reference data 83. Also, it is allowable that
the shading amending reference data 83 are calculated and stored in
advance using the host computer connected with the general control
unit 104 over the network, and then are downloaded at the time of
starting the inspection so that the CPU in the shading amending
circuit 74 can capture the downloaded data. In the shading amending
circuit 74, there are provided two aspects of amendment memories
with the number of pixels in a deflected width of an ordinary
electron beam (for example, 1024 pixels). concerning whole visual
field correspondence, the correspondence is achieved by switching
each of the memories during the time of executing no inspection
(i.e. the time interval from when one visual field inspection is
over and the next one visual field inspection is started).
Installed as the amendment data are the one with the number of
pixels in a maximum deflected width of the electron beam (for
example, 5000 pixels). The CPU achieves the correspondence by
rewriting the data in each of the amendment memories by the time
the next one visual field inspection is over.
[0058] As described above, performed to the digital image data
(gradation image data) 71 obtained by the electricity converting
means (light receiving device) 125 are the following amendments,
i.e. the dark level amendment (the dark level is amended with
reference to the detection signal 71 during the beam-blanking
period), the electron source fluctuation amendment (intensity of
the beam current is monitored, and the signal is normalized using
the beam current), and the shading amendment (the variations in
light quantity due to the beam scanning position are amended).
After that, performed to the amended digital image data (gradation
image data) 80 in order to improve the image quality is a filtering
process in a filtering process circuit 81 by means of a Gaussian
filter, an average value filter, and an edge emphasizing filter,
and so on. Distortion of the image, if required, is also amended
These preprocessings are carried out to convert the detection
images so that they will be advantageous and helpful to a defect
judging process later.
[0059] A delay circuit 41, which comprises units such as shift
registers, delays by a constant time an amended digital image data
(gradation image data) 82 the image quality of which has been
improved by the preprocessing circuit 40. If the delay time, which
is obtained from the general control unit 104, is made equal to a
time during which, for example, the stage 2 moves by a chip pitch
(d1 in FIG. 2), a delayed signal g0 and an undelayed signal f0
become image signals at a same place in chips neighboring to each
other. This turns out to be the chip comparison inspection
described above. Otherwise, if the delay time, which is obtained
from the general control unit 104, is made equal to a time during
which the stage 2 moves by a pitch of a memory cell (d2 in FIG. 2),
a delayed signal g0 and an undelayed signal f0 become image signals
at a same place in memory cells neighboring to each other. This
turns out to be the cell comparison inspection described above. In
this way, the delay circuit 41 is configured so that it can select
an arbitrary delay time by controlling a position of a pixel to be
read, based on information obtained from the general control unit
104. As is described above, the digital image data (gradation image
data) f0 and g0, which are to be compared with each other, are
fetched from the image fetching unit 102. Hereinafter, f0 and g0
are referred to as a detection image and a comparison image,
respectively. Incidentally, as shown in FIG. 11, it is allowable to
store the comparison image signal g0 in a first image memory unit
146 comprising units such as the shift registers and the image
memories and to store the detection image signal f0 in a second
image memory unit 147 comprising units such as the shift registers
and the image memories. As described above, the first image memory
unit 146 may comprise the delay circuit 41, and the second image
memory unit 147 is not necessarily required.
[0060] Also, it is possible to display on the monitor 150 and
observe the electron beam images captured in units such as the
preprocessing circuit 40 and the second image memory unit 147, or
the optical images detected by the optical microscope unit 108.
[0061] Describe next, using FIG. 1, is an image processing unit
103a.
[0062] Obtained from the preprocessing unit 40 is a detection image
f0(x,y) represented by a gradation value (a value of light and
shade) about an inspection area on the object to be inspected 100.
Obtained from the delay circuit 41 is a comparison image (criterion
image: reference image) g0(x,y) represented by a gradation value (a
value of light and shade) about an inspection area on the object to
be inspected 100, which becomes a criterion on which the comparison
is made.
[0063] In a pixel unit of position alignment unit 42, a position
of, for example, the comparison image is shifted so that a position
shift quantity of the comparison image g0(x,y) with reference to
the above-mentioned detection image f0(x,y) falls within 0 to 1
pixel, in other words, a position at which "compatibility" (i.e.
the degree of matching) between f0(x,y) and g0(x,y) becomes its
maximum falls within 0 to 1 pixel. As a result, it turns out that,
as shown in FIG. 3, position alignment has been made with one pixel
unit or less of accuracy between the detection image f0(x,y) and
the comparison image g0(x,y). The pixel is indicated by a square
shown by a chain line in FIG. 3. The pixel is a unit which is
detected by the electron detector 35, undergoes a sampling by means
of the A/D converter 39, and is converted into the digital value
(the gradation value : the value of light and shade). Namely, the
pixel unit is a minimum unit of the images which can be detected by
the electron detector 35. Incidentally, considered as the
above-described "compatibility" can be expressions such as the
following formula 1,
max.vertline.f0-g0, .SIGMA..SIGMA..vertline.f0-g0.vertline.,
.SIGMA..SIGMA.(f0-g0).sup.2 (1)
[0064] where max.vertline.f0-g0.vertline. shows a maximum of
absolute value of a difference between the detection image f0(x,y)
and the comparison image g0(x,y).
.SIGMA..SIGMA..vertline.f0-g0.vertline. indicates a summation of
the difference between the detection image f0(x,y) and the
comparison image g0(x,y) within the images.
.SIGMA..SIGMA.(f0-g0).sup.2 shows a value obtained by integrating
in a x-direction and a y-direction a square of the difference
between the detection image f0(x,y) and the comparison image
g0(x,y).
[0065] Content to be processed varies, depending on which of the
formula 1 is employed. Shown here is a case in which
.SIGMA..SIGMA..vertline.f0-g0.- vertline. is employed.
[0066] Assuming that m.sub.x and m.sub.y are shift quantities of
the comparison image g0(x,y) in a x-direction and a y-direction,
respectively (where m.sub.x and m.sub.y are integers), quantities
e1(m.sub.x,m.sub.y) and s1(m.sub.x,m.sub.y) are defined as the
expressions (2) and (3) described below.
e1(m.sub.x,m.sub.y)=.SIGMA..SIGMA..vertline.f0(x,y)-g0(x+m.sub.x,y+m.sub.y-
).vertline. (2)
s1(m.sub.x,m.sub.y)=e1(m.sub.x,m.sub.y)+e1(m.sub.x+1,m.sub.y)+e1(m.sub.x,m-
.sup.y+1)+e1(m.sub.x+1,m.sub.y+1) (3)
[0067] In the equation (2), .SIGMA..SIGMA. indicates the summation
within the image. What is needed here are values of the shift
quantity m.sub.x in a x-direction and the shift quantity m.sub.y in
a y-direction at which s1(m.sub.x,m.sub.y) becomes its minimum.
Accordingly, by changing each of m.sub.x and m.sub.y in such a way
as .+-.0, 1, 2, 3, 4 . . . n, in other words, by shifting the
comparison image g0(x,y) by the pixel pitch, s1(m.sub.x, m.sub.y)
at each time is calculated. Then, values of m.sub.x0 and m.sub.y0
out of m.sub.x and m.sub.y, at which it becomes its minimum, are
determined. Additionally, since n is a maximum shift quantity of
the comparison image, it is necessary to make, depending on
position accuracy of the detecting unit 101, the value of n even
larger as the position accuracy gets worse. From the pixel unit of
position alignment unit 42, the detection image f0(x,y) is
outputted just as it is, and the comparison image g0(x,y) is
outputted with shift applied by (m.sub.x0,m.sub.y0). Namely, this
is expressed by the relations,
f1(x,y)=f0(x,y),
g1(x,y)=g0(x+m.sub.x0,y+m.sub.y0).
[0068] In a one pixel or less of shift detecting unit 43, the
images f1(x,y) and g1(x,y), over which the position alignment has
been performed in the pixel unit, are divided into small areas (for
example, a partial image consisting of 128*256 pixels), and
position shift quantity of one pixel or less (the position shift
quantity becomes a real number within a range of 0 to 1) is
calculated for each divided area (the partial image). The division
into the small areas is made in order to correspond to distortions
of the images, and it is needed to arrange an area which is small
enough to be able to neglect the distortion therein. Employed as a
measure of the compatibility can also be the alternatives shown in
the formula 1. Shown here is a case in which the third expressions,
i.e. "a summation of square of the difference"
(.SIGMA..SIGMA.(f0-g0).sup.2) is employed.
[0069] Assuming that the position shift quantity is equal to zero
at an intermediate position between f1(x,y) and g1(x,y), and, as
shown in FIG. 3, f1 is shifted by -.delta.x in a x-direction and by
-.delta.y in a y-direction, and g1 is shifted by +.delta.x in a
x-direction and by +.delta.y in a y-direction. Namely, it is
considered that the position shift quantity between f1(x,y) and
g1(x,y) is 2*.delta.x in a x-direction and 2*.delta.y in a
y-direction. Since .delta.x and .delta.y are no integers, it is
required to define a value between two pixels in order to shift the
images by .delta.x or .delta.y. Defined as the following
expressions (4) and (5) are an image f2, which is obtained by
shifting f1 by +.delta.x in a x-direction and by +.delta.y in a
y-direction, and an image g2, which is obtained by shifting g1 by
-.delta.x in a x-direction and by -.delta.y in a y-direction.
f2(x,y)=f1(x+.delta.x,y+.delta.y)=f1(x,y)+.delta.x(f1(x+1,y)-f1(x,y))+.del-
ta.y(f1(x,y+1)-f1(x,y)) (4)
g2(x,y)=g1(x-.delta.x,y-.delta.y)=g1(x,y)+.delta.x(g1(x-1,y)-g1(x,y))+.del-
ta.y(g1(x,y-1)-g1(x,y)) (5)
[0070] The expressions (4) and (5) are based on so-called a linear
interpolation. When employing "a summation of square of the
difference", e2(.delta.x, .delta.y), i.e. the compatibility between
f2 and g2 turns out to be the following expression (6).
e2(.delta.x,.delta.y)=.SIGMA..SIGMA.(f2(x,y)-g2(x,y)).sup.2 (6)
[0071] .SIGMA..SIGMA. is a summation within the small area (the
partial area). An object of the one pixel or less of shift
detecting unit 43 is to determine values of .delta.x0 of .delta.x
and .delta.y0 of .delta.y at which e2(.delta.x, .delta.y) becomes
its minimum. Setting to be zero expressions obtained by partially
differentiating the above-mentioned expression (6) with .delta.x,
.delta.y and solving them with respect to .delta.x, .delta.y, the
values have been found to be the formulas (7) and (8) described
below.
.delta.x={(.SIGMA..SIGMA.C0*Cy)*(.SIGMA..SIGMA.Cx*Cy)-(.SIGMA..SIGMA.C0*Cx-
)*(.SIGMA..SIGMA.Cy*Cy)}/{(.SIGMA..SIGMA.Cx*Cx)*(.SIGMA..SIGMA.Cy*Cy)-(.SI-
GMA..SIGMA.Cx*Cy)*(.SIGMA..SIGMA.Cx*Cy)} (7)
.delta.y={(.SIGMA..SIGMA.C0*Cx)*(.SIGMA..SIGMA.Cx*Cy)-(.SIGMA..SIGMA.C0*Cy-
)*(.SIGMA..SIGMA.Cx*Cx)}/{(.SIGMA..SIGMA.Cx*Cx)*(.SIGMA..SIGMA.Cy*Cy)-(.SI-
GMA..SIGMA.Cx*Cy)*(.SIGMA..SIGMA.Cx*Cy)} (8)
[0072] where C0, C x, and C y are given by the following relations
(9), (10), and (11), respectively.
C0=f1(x,y)-g1(x,y) (9)
Cx={f1(x+1,y)-f1(x,y)}-{g1(x-1,y)-g1(x,y)} (10)
Cy={f1(x,y+1)-f1(x,y)}-{g1(x,y-1)-g1(x,y)} (11)
[0073] In order to determine .delta.x0 and .delta.y0, as shown in
the formulas (7) and (8), it is required to determine the
above-mentioned variety kinds of statistical quantities
.SIGMA..SIGMA.Ck*Ck (where Ck=C0, Cx, and Cy). Based on the
detection image f1(x,y) and the comparison image g1(x,y) consisting
of the gradation values (the values of light and shade), which are
obtained from the pixel unit of position alignment unit 42 and over
which the position alignment has been performed in the pixel unit,
a statistical quantity calculating unit 44 calculates the variety
kinds of statistical quantities .SIGMA..SIGMA.Ck*Ck.
[0074] Using .SIGMA..SIGMA.Ck*Ck calculated by the statistical
quantity calculating unit 44, a sub CPU executes arithmetic
computation of the above-described expressions (7) and (8) so as to
determine .delta.x0 and .delta.y0.
[0075] Delay circuits 46 and 47, which comprise units such as shift
registers, delay the image signals f1 and g1 by a time period that
the one pixel or less of position shift detecting unit 43 needs to
determine .delta.x0 and .delta.y0.
[0076] Determined by a difference image extracting circuit (a
finite difference extracting circuit a distance extracting unit) 49
is sub (x,y), i.e. a difference image (a distance image) between f1
and g1 which has a position shift of 2*.delta.x0 and 2*.delta.y0 in
calculation. The difference image (the distance image) sub (x,y) is
expressed by the expression (12) as follows.
sub(x,y)=g1(x,y)-f1(x,y) (12)
[0077] Using the image signals f1 and g1 which have passed through
the delay circuits 46 and 47 and the one pixel or less of position
shift quantities .delta.x0 and .delta.y0 obtained by the one pixel
or less of position shift detecting unit 43, a threshold arithmetic
circuit (an allowable range arithmetic unit) 48 calculates two
threshold values (allowable values indicating allowable range)
thH(x, y) and thL(x, y), which a defect judging circuit (a defect
judging unit) 50 uses to determine whether or not the pixel is a
defective candidate depending on a value of the difference image
(the distance image) sub (x, y) obtained from the difference image
extracting circuit (the finite difference extracting circuit: the
distance extracting unit) 49. Then, thH(x, y) is a threshold value
(allowable value indicating allowable range) defining an upper
limit of the difference image (the distance image) sub (x, y), and
thL(x, y) is a threshold value (allowable value indicating
allowable range) defining a lower limit of the difference image
(the distance image) sub (x, y). Shown in FIG. 5 is a configuration
of the threshold arithmetic circuit 48. Content of the arithmetic
operation in the threshold arithmetic circuit 48 is expressed by
the expressions (12) and (13) as follows.
thH(x,y)=A(x,y)+B(x,y)+C(x,y) (13)
thL(x,y)=A(x,y)-B(x,y)-C(x,y) (14)
[0078] Here, A(x,y) is a term which is given by the following
relation (15) and has a function of substantially amending the
threshold values with the use of the one pixel or less of position
shift quantities .delta.x0 and .delta.y0 in correspondence with a
value of the difference image (the distance image) sub (x,y).
[0079] Also, B(x,y) is a term which is given by the following
relation (16) and has a function of allowing an infinitesimal
position shift of pattern edges (an infinitesimal difference in the
pattern configuration and distortion in the patterns are attributed
to the infinitesimal position shift of pattern edges from a local
point of view) between the detection image f1 and the comparison
image g1.
[0080] C(x,y) is a term which is given by the following relation
(17) and has a function of allowing an infinitesimal difference in
the gradation value (the value of light and shade) between the
detection image f1 and the comparison image g1.
A(x,y)={dx1(x,y)*.delta.x0-dx2(x,y)*(-.delta.x0)}+{dy1(x,y)*.delta.y0-dy2(-
x,y)*(-.delta.y0)y={dx1(x,y)+dx2(x,y)}*.delta.x0+{dy1(x,y)+dy2(x,y)}.delta-
.y0 (15)
B(x,y)=.vertline.{dx1(x,y)*.alpha.-dx2(x,y)*(-.alpha.)}.vertline.+.vertlin-
e.{dy1(x,y)*.beta.-dy2(x,y)*(-.beta.)}.vertline.=.vertline.{dx1(x,y)+dx2(x-
,y)}*.alpha..vertline.+.vertline.{dy1(x,y)+dy2(x,y)}*.beta..vertline.
(16)
C(x,y)=((max1+max2)/2)*.gamma.+.epsilon. (17)
[0081] Where .alpha. and .beta. are real numbers within a range of
0 to 0.5, .gamma. is a real number greater than zero, and .epsilon.
is an integer greater than zero.
[0082] Also, dx1(x,y), which is given by the following relation
(18), indicates a variation amount in the gradation value (the
value of light and shade) in the detection image f1(x,y) between an
image and an image which is +1 proximate thereto in a
x-direction,
[0083] dx2(x,y), which is given by the following relation (19),
indicates a variation amount in the gradation value (the value of
light and shade) in the detection image g1(x,y) between an image
and an image which is -1 proximate thereto in a x-direction,
[0084] dy1(x,y), which is given by the following relation (20),
indicates a variation amount in the gradation value (the value of
light and shade) in the detection image f1(x,y) between an image
and an image which is +1 proximate thereto in a y-direction,
and
[0085] dy2(x,y), which is given by the following relation (21),
indicates a variation amount in the gradation value (the value of
light and shade) in the detection image g1(x,y) between an image
and an image which is -1 proximate thereto in a y-direction.
dx1(x,y)=f1(x+1,y)-f1(x,y) (18)
dx2(x,y)=g1(x,y)-g1(x-1,y) (19)
dy1(x,y)=f1(x,y+1)-f1(x,y) (20)
dy2(x,y)-g1(x,y)-g1(x,y-1) (21)
[0086] Also, max1, which is given by the following relation (22),
indicates a maximum in the gradation value (the value of light and
shade) in the detection image f1(x,y) among an image, an image
which is +1 proximate thereto in a x-direction, and an image which
is +1 proximate thereto in a y-direction, and max2, which is given
by the following relation (23), indicates a maximum in the
gradation value (the value of light and shade) in the comparison
image g1(x,y) among an image, an image which is -1 proximate
thereto in a x-direction, and an image which is -1 proximate
thereto in a y-direction.
max1=max{f1(x,y),f1(x+1,y),f1(x,y+1),f1(x+1,y+1)} (22)
max2=max{g1(x,y),g1(x-1,y),g1(x,y-1),g1(x-1,y-1)} (23)
[0087] Described first is the first term A(x,y) in the expressions
(13) and (14) for calculating the threshold values thH(x,y) and
thL(x,y). Namely, the first term A(x,y) in the expressions (13) and
(14) for calculating the threshold values thH(x,y) and thL(x,y) is
a term for amending the threshold values in correspondence with the
one pixel or less of position shift quantities .delta.x0 and
.delta.y0 determined by the one pixel or less of position shift
detecting unit 43. Since, for example, dx1 expressed in the
expression (18) is a local variation rate in the gradation value
off f1 in a x-direction, dx1(x,y)*.delta.x0 shown in the expression
(15) can be said to be a predicted value of a variation in the
gradation value (the value of light and shade) of f1 when the
position is shifted by .delta.x0. Consequently, the first term
{dx1(x,y)*.delta.x0-dx2(x,y)*(-.delta.x0)} shown in the expression
(15) can be said to be a value of predicting to what extent the
gradation value (the value of light and shade) of the difference
image (the distance image) between f1 and g1 is varied for each
pixel when the position of f1 is shifted by .delta.x0 and the
position of g1 is shifted by -.delta.x0 in a x-direction.
Similarly, the second term can be said to be a value of the
prediction about a y-direction. Namely,
{dx1(x,y)+dx2(x,y)}*.delta.x0 is a value of predicting to what
extent the gradation value (the value of light and shade) of the
difference image (the distance image) between f1 and g1 is varied
for each pixel a x-direction when {dx1(x,y)+dx2(x,y)}, i.e. a local
variation rate in the difference image (the distance image) between
the detection image f1 and the comparison image g1 in a
x-direction, is multiplied by the position shift .delta.x0.
Similarly, {dy1(x,y)+dy2(x,y)}*.delta.y0 is a value of predicting
to what extent the gradation value (the value of light and shade)
of the difference image (the distance image) between f1 and g1 is
varied for each pixel in a y-direction when {dy1(x,y)+dy2(x,y)},
i.e. a local variation rate in the difference image (the distance
image) between the detection image f1 and the comparison image g1
in a y-direction, is multiplied by the position shift
.delta.y0.
[0088] As explained above, the first term A(x,y) in the expressions
for the threshold values thH(x,y) and thL(x,y) is a term for
canceling the known position shift quantities .delta.x0 and
.delta.y0.
[0089] Described next is the second term B(x,y) in the expressions
(13) and (14) for calculating the threshold values thH(x,y) and
thL(x,y). Namely, the second term B(X,y) in the expressions (13)
and (14) for calculating the threshold values thH(x,y) and thL(x,y)
is a term for allowing an infinitesimal position shift of pattern
edges (an infinitesimal difference in the pattern configuration and
distortion in the patterns are attributed to the infinitesimal
position shift of pattern edges from a local point of view). As is
apparent from the comparison between the expression (15) for
determining A(x,y) and the expression (16) for determining B(x,y),
B(x,y) is an absolute value of the predicted variation in the
gradation value (the value of light and shade) of the difference
image (the distance image) by means of the position shifts
.delta.x0 and .delta.y0. If it is assumed that A(x,y) cancels the
position shifts, adding B(x,y) to A(x,y) means the following. From
a state in which the positions coincides with each other, the
positions are shifted by .alpha. in a x-direction and by .beta. in
a y-direction, taking into consideration the infinitesimal position
shift of the pattern edges caused by an infinitesimal difference
due to the pattern configuration and the distortion in the
patterns. Namely, +B(x,y) shown in the above-mentioned expression
(13) allows +.alpha. in a x-direction and +.beta. in a y-direction
as the infinitesimal position shift of the pattern edges caused by
an infinitesimal difference due to the pattern configuration and
the distortion in the patterns. Also, as shown in the
above-mentioned expression (14), subtracting B(x,y) from A(x,y)
means that, from the state in which the positions coincides with
each other, the positions are further shifted by -.alpha. in a
x-direction and by -.beta. in a y-direction. Namely, -B(x,y) shown
in the abovementioned expression (14) allows the position shifts by
-.alpha. in a x-direction and by -.beta. in a y-direction,
respectively. After all, as shown in the above-mentioned
expressions (13) and (14), the position shift by .+-..alpha. and
.+-..beta. are allowed by providing the threshold with the upper
limit thH(x,y) and the lower limit thL(x,y). Moreover, in the
threshold arithmetic circuit 48, values of the parameters .alpha.
and .beta. inputted are set to be appropriate values. This makes it
possible to freely control the allowed position shift quantities
caused by an infinitesimal difference due to the pattern
configuration and the distortion in the patterns (the infinitesimal
position shift of the pattern edges).
[0090] Described next is the third term C(x,y) in the expressions
(13) and (14) for calculating the threshold values thH(x,y) and
thL(x,y). Namely, the third term C(x,y) in the expressions (13) and
(14) for calculating the threshold values thH(x,y) and thL(x,y) is
a term for allowing an infinitesimal difference in the gradation
value (the value of light and shade) between the detection image f1
and the comparison image g1. As shown in the expression (13), what
the addition of C(x,y) means is to allow that the gradation value
(the value of light and shade) of the comparison image g1 is
greater by C (x,y) than the gradation value (the value of light and
shade) of the detection image f1. As shown in the expression (14),
what the subtraction of C(x,y) means is to allow that the gradation
value (the value of light and shade) of the comparison image g1 is
smaller by C(x,y) than the gradation value (the value of light and
shade) of the detection image f1. In the present invention, as
shown in the expression (17), C(x,y) is set to be a summation of a
constant .epsilon. and a value obtained by multiplying a
representative value of the gradation value in the local area (a
maximum value here) by a proportionality constant .gamma.. There is
no need of sticking to this function, however. As long as the way
the gradation value varies is known, it is much better to select a
function suitable therefor. If, for example, it is known that a
width of the variation is proportional to a square root of the
gradation value, the expression (17) should be replaced by the
expression c(x,y)=(square root of (max1+max2))*.gamma.+.e- psilon..
In the threshold arithmetic circuit 48, as is the case with B(x,y),
it becomes possible to freely control the difference in the allowed
gradation value (the value of light and shade) by setting values of
the parameters .gamma. and .epsilon. to be appropriate values.
[0091] The threshold arithmetic circuit (allowable range arithmetic
unit) 48, as shown in FIG. 5, comprises an arithmetic circuit 91
which, based on the detection image f1(x,y) consisting of the
gradation value (the value of light and shade) inputted from the
delay circuit 46 and the comparison image g1(x,y) consisting of the
gradation value (the value of light and shade) inputted from the
delay circuit 47, performs an arithmetic operation of
{dx1(x,y)+dx2(x,y)} using the expressions (18) and (19), an
arithmetic circuit 92 which performs an arithmetic operation of
{dy1(x,y)+dy2(x,y)} using the expressions (20) and (21), and an
arithmetic circuit 93 which performs an arithmetic operation of
(max1+max2) using the expressions (22) and (23). The threshold
arithmetic circuit 48 further comprises an arithmetic circuit 94
which, based on {dx1(x,y)+dx2(x,y)} obtained by the arithmetic
circuit 91, .delta.x0 obtained by the one pixel or less of position
shift detecting unit 43, and a parameter .alpha. to be inputted,
performs an arithmetic operation of
({dx1(x,y)+dx2(x,y)})*.delta.x0.+-..vertline.{dx1(x,
y)+dx2(x,y)}.vertline.*.alpha.), i.e. a portion of the expression
(15) and a portion of the expression (16), an arithmetic circuit 95
which, based on {dy1(x,y)+dy2(x,y)} obtained by the arithmetic
circuit 92, .delta.y0 obtained by the one pixel or less of position
shift detecting unit 43, and a parameter 13 to be inputted,
performs an arithmetic operation of
({dy1(x,y)+dy2(x,y)}*.delta.y0.+-..vertline.dy1(x,y)+dy2(x,y-
)}.vertline.*.beta.),i.e. a portion of the expression (15) and a
portion of the expression (16), and an arithmetic circuit 96 which,
based on (max1+max2) obtained by the arithmetic circuit 93 and
parameters .gamma. and .epsilon. to be inputted, performs an
arithmetic operation of ((max1+max2)/2)*.gamma.+.epsilon.)
following, for example, the expression (17). The threshold
arithmetic circuit 48 still further comprises an adding circuit 98
which outputs the upper limit of the threshold thH(x,y) by
performing +arithmetic operation of
({dx1(x,y)+dx2(x,y)}*.delta.x0+.ve-
rtline.{dx1(x,y)+dx2(x,y)}.vertline.*.alpha.) obtained by the
arithmetic circuit 94,
({dy1(x,y)+dy2(x,y)}*.delta.y0+.vertline.{dy1(x,y)+dy2(x,y)}.-
vertline.*.beta.) obtained by the arithmetic circuit 95, and
((max1+max2)/2) *.gamma.+.epsilon.) obtained by the arithmetic
circuit 96, a subtracting circuit 97 which performs--arithmetic
operation of ((max1+max2)/2)* .gamma.+.epsilon.) obtained by the
arithmetic circuit 96, and an adding circuit 99 which outputs the
lower limit of the threshold thL(x, y) by performing +arithmetic
operation of
({dx1(x,y)+dx2(x,y)}*.delta.x0-.vertline.{dx1(x,y)+dx2(x,y)}.vertline.*.a-
lpha.) obtained by the arithmetic circuit 94,
({dy1(x,y)+dy2(x,y)}*.delta.-
y0-.vertline.{dy1(x,y)+dy2(x,y)}.vertline.*.beta.) obtained by the
arithmetic circuit 95, and -((max1+max2)/2)*.gamma.+.epsilon.)
obtained by the subtracting circuit 97.
[0092] Incidentally, the threshold arithmetic circuit 48 can also
be embodied by the CPU through a soft processing thereof. It is
also allowable that the parameters to be inputted into the
threshold arithmetic circuit 48 are inputted by using an inputting
means provided in the general control unit 104 (for example, an
inputting means comprising a keyboard, a recording medium, a
network, and so on).
[0093] Using the difference image (the distance image) sub (x,y)
obtained from the difference image extracting circuit (the finite
difference extracting circuit) 49, the threshold value at the lower
limit thL(x,y) (an allowable value indicating the lower limit
within the allowable range) and the threshold value at the upper
limit thH(x,y) (an allowable value indicating the upper limit
within the allowable range) obtained from the threshold arithmetic
circuit 48, the defect judging circuit (the defect judging unit) 50
judges a pixel at the position (x,y), if the following relation
(24) is satisfied, to be an non-defective candidate, and the pixel
at the position (x,y), if the following relation (24) is not
satisfied, to be a defective candidate. The defect judging circuit
50 outputs, for the non-defective candidate pixel, def(x,y) having
a value of, for example, zero, and outputs, for the defective
candidate pixel, def(x,y) having a value of, for example, one or
more indicating the mismatched quantity.
thL(x,y)<sub(x,y).ltoreq.thH(x,y) (24)
[0094] In a characteristic extracting circuit 50a, after a
noise-like (for example, all of the 3.times.3 pixels are not the
defective candidate pixels at the same time) output is eliminated
by a noise eliminating process (For example, a processing of
downsizing/upsizing for def(x,y) is performed. For example, when
all of the 3.times.3 pixels are not the defective candidate pixels
at the same time, a pixel in the center thereof is made equal to
zero (the non-defective candidate pixel) and eliminated by
performing the downsizing process, and then it is restored back to
the original by performing the upsizing process.), a merge
processing of the defective candidate parts, which summarizes the
neighboring defective candidate parts into a group, is carried out.
After that, the characteristic extracting circuit 50a calculates
and outputs, for each group, characteristic quantities 88 such as a
coordinate of the center of gravity, XY projection length (This
quantity shows maximum lengths in a x-direction and a y-direction.
Additionally, a square root of (a square of X projection length+a
square of Y projection length) becomes the maximum length), and the
area.
[0095] As explained above, obtained from the controlled by the
general control unit 104 are the characteristic quantities 88 (for
example, the coordinate of the center of gravity, the XY projection
length, the area, and so on) of the defective candidate parts in
correspondence with coordinates on the object to be inspected
(sample) 100 irradiated with an electron beam and detected by the
electron detector 35.
[0096] The general control unit 104 converts position coordinates
of the defective candidate parts on the detection image into
coordinate system on the object to be inspected (sample) 100 and
deletes pseudo defects, finally summarizing data on the defects
consisting of the positions on the object to be inspected (sample)
100 and the characteristic quantities calculated by the
characteristic extracting circuit 50a in the image processing unit
103a.
[0097] The present embodiment allows a position shift of a small
area (the partial image) as a whole, an infinitesimal position
shift of an individual pattern edge, and an infinitesimal
difference in the gradation value (the value of light and shade).
This prevents a possibility of misjudging the normal part to be a
defect. Also, it becomes possible to freely control allowable
values of the position shifts and variations in the gradation
values by setting the parameters .alpha., .beta., .gamma. and
.epsilon. to be appropriate values.
[0098] Also, in the present embodiment, unlike the above-described
prior art (Japanese Laid-Open Patent Publication No. Hei 3-177040),
it is not carried out to generate, by employing interpolation,
images the positions of which coincide with each other in a pseudo
way. This prevents a smoothing effect of the images, which is
difficult to avoid in the interpolation, and thus brings about an
merit of making it advantageous to detect an infinitesimal defect.
Actually, the inventors et al. has made the following experiment.
After the images the positions of which coincide with each other in
a pseudo way are generated by the interpolation with the use of a
result of the one pixel or less of position shift detection, a
defect judgment is made by, as is the case with the present
embodiment, calculating the threshold values allowing the position
shifts and variations in the gradation values. Eventually, the
experiment has shown a 5% or more of increase in performance of
detecting a defect, when comparing a result obtained in the
above-mentioned manner with a result obtained by making a defect
judgment according to the present embodiment.
[0099] Modifications of the First Embodiment
[0100] In a first modification of the first embodiment, as shown in
FIG. 6, no pixel unit of position alignment is performed. When the
detecting unit 101 detects an image with a high position accuracy
and a position error of the detected image is less than one pixel,
the pixel unit of position alignment is unnecessary, and one pixel
or less of position shift detection should be performed
immediately. Namely, the configuration in which the first
modification shown in FIG. 6 differs from the first embodiment
shown in FIG. 1 is that, since the detecting unit 101 detects an
image with a high position accuracy and a position error of the
detected image is less than one pixel, there is provided an image
processing unit 103b without the pixel unit of position alignment
unit 42. In the first modification, too, the threshold arithmetic
circuit 48 outputs a threshold value at an upper limit thH(x,y) (an
allowable value indicating the upper limit within an allowable
range) based on the equation (13) and a threshold value at a lower
limit thL(x,y) (an allowable value indicating the lower limit
within an allowable range) based on the equation (14). Using the
difference image (the distance image) sub (x,y) obtained from the
difference image extracting circuit (the finite difference
extracting circuit) 49, the threshold value at the lower limit
thL(x,y) (an allowable value indicating the lower limit within the
allowable range) and the threshold value at the upper limit
thH(x,y) (an allowable value indicating the upper limit within the
allowable range) obtained from the threshold arithmetic circuit 48,
the defect judging circuit (the defect judging unit) 50 judges a
pixel at the position (x,y), if the above-mentioned relation (24)
is satisfied, to be an non-defective candidate, and the pixel at
the position (x,y), if the above-mentioned relation (24) is not
satisfied, to be a defective candidate. The defect judging circuit
50 outputs, for the non-defective candidate pixel, def(x,y) having
a value of, for example, zero, and outputs, for the defective
candidate pixel, def(x,y) having a value of, for example, one or
more indicating the mismatched quantity. Moreover, in the
characteristic extracting circuit 50a, after a noise-like output is
eliminated by a noise eliminating process (For example, a
processing of downsizing/upsizing for def(x,y) is performed.), a
merge processing of the defective candidate parts, which summarizes
the neighboring defective candidate parts into a group, is carried
out. After that, the characteristic extracting circuit 50a
calculates and outputs, for each group, characteristic quantities
88 such as the coordinate of the center of gravity, the XY
projection length, and the area.
[0101] In a second modification of the first embodiment, as shown
in FIG. 7, neither the pixel unit of position alignment or the one
pixel or less of position shift detection is performed. When the
detecting unit 101 detects an image with an even higher position
accuracy and a position error of the detected image is
substantially negligible, even the one pixel or less of position
shift detection becomes unnecessary. Namely, the configuration in
which the second modification shown in FIG. 7 differs from the
first embodiment shown in FIG. 1 is that, since the detecting unit
101 detects an image with an even higher position accuracy and a
position error of the detected image is substantially negligible,
there are removed the pixel unit of position alignment unit 42 and
the one pixel or less of position shift detecting unit 43. Instead,
there is provided an image processing unit 103c having a sub CPU
45. The sub CPU 45 outputs .omega., i.e. a fractional portion of a
value obtained by dividing a comparison interval P by a pixel size
e, which is introduced from the general control unit 140. It is
assumed that P designates a comparison interval between the images
(in the case of the chip comparison, an interval between the chips
to be compared, and in the case of the cell comparison, an interval
between the memory cells to be compared), e designates a pixel
size, and .omega.x and .omega.y designate a fractional portion of a
value obtained by dividing the comparison interval P by the pixel
size e. In this case, .delta.x and .delta.y, which are obtained as
the result of the one pixel or less of position shift detection,
are replaced by .omega.x/2 and .omega.y/2. Namely, it becomes
necessary to obtain A(x, y), using the following expression
(15').
A(x,y)={dx1(x,y)*.omega.x/2-dx2(x,y)*(-.omega.x/2)}+{dy1(x,y)*.omega.y/2-d-
y2(x,y)*(-.omega.y/2)}={dx1(x,y)+dx2(x,y)}*.omega.x/2+{dy1(x,y)+dy2(x,y)}*-
.omega.y/2 (15')
[0102] In the second modification, too, the threshold arithmetic
circuit 48 outputs a threshold value at an upper limit thH(x,y) (an
allowable value indicating the upper limit within an allowable
range) based on the equation (13) and a threshold value at a lower
limit thL(x,y) (an allowable value indicating the lower limit
within an allowable range) based on the equation (14). Using the
difference image (the distance image) sub(x,y) obtained from the
difference image extracting circuit (the finite difference
extracting circuit) 49, the threshold value at the lower limit
thL(x,y) (an allowable value indicating the lower limit within the
allowable range) and the threshold value at the upper limit
thH(x,y) (an allowable value indicating the upper limit within the
allowable range) obtained from the threshold arithmetic circuit 48,
the defect judging circuit (the defect judging unit) 50 judges a
pixel at the position (x,y), if the above-mentioned relation (24)
is satisfied, to be an non-defective candidate, and the pixel at
the position (x,y), if the above-mentioned relation (24) is not
satisfied, to be a defective candidate. The defect judging circuit
50 outputs, for the non-defective candidate pixel, def(x,y) having
a value of, for example, zero, and outputs, for the defective
candidate pixel, def(x,y) having a value of, for example, one or
more indicating the mismatched quantity. Moreover, in the
characteristic extracting circuit 50a, after a noise-like output is
eliminated by a noise eliminating process (For example, a
processing of downsizing/upsizing for def(x,y) is performed.), a
merge processing of the defective candidate parts, which summarizes
the neighboring defective candidate parts into a group, is carried
out. After that, the characteristic extracting circuit 50a
calculates and outputs, for each group, characteristic quantities
88 such as the coordinate of the center of gravity, the XY
projection length, and the area.
[0103] In a third modification of the first embodiment, the one
pixel or less of position shift quantity is determined in the
following way, instead of determining them as shown in the
expressions (4) to (11). Determined first are a summation (an
extent over which the summation is taken is the one for each small
area) of square of a difference in the gradation values (the values
of light and shade) of the image f1 and the image g1 in a state in
which the position alignment has been performed between f1 and g1
for each pixel, and a summation (an extent over which the summation
is taken is the one for each small area) of square of the
difference when g1 is shifted with reference to f1 in a variety of
directions by an integer multiple of the pixel. Defined next, based
on interpolation between theses summations, is a summation of
square of the difference when g1 is shifted with reference to f1 by
one pixel or less of arbitrary quantity. Employed as the position
shift quantity to be calculated is a shift quantity to which the
summation defined turns out to be its minimum. Otherwise, used
instead of the summation of square of the difference are a
summation of absolute value of the difference or a normalized
correlation.
[0104] A fourth modification of the first embodiment is a
modification concerning a calculating method on the expressions
(13) to (23).
[0105] The expressions (18) to (21) are replaced by the following
expressions (25) to (28).
dx1(x,y)=[{f1(x+1,y)+f1(x+1,y+1)}-{f1(x,y)+f1(x,y+1)}]/2 (25)
dx2(x,y)=[{g1(x,y)+g1(x,y-1)}-{g1(x-1,y)+g1(x-1,y-1}]/2 (26)
dy1(x,y)=[{f1(x,y+1)+f1(x+1,y+1)}-{f1(x,y)+f1(x+1,y)}]/2 (27)
dy2(x,y)=[{g1(x,y)+g1(x-1,y)}-{g1(x,y-1)+f1(x-1,y-1)}]/2 (28)
[0106] Otherwise, the expressions (18) to (21) are replaced by the
following expressions (29) to (30).
dx1(x,y)=dy1(x,y)=max{f1(x,y), f1(x+1,y), f1(x,y+1), f1(x+1,
y+1)}-min{f1(x,y), f1(x+1,y), f1(x,y+1), f1(x+1, y+1)} (29)
dx2(x,y)=dy2(x,y)=max{g1(x,y), g1(x-1,y), g1(x,y-1),
g1(x-1,y-1)}-min{g1(x,y), g1(x-1,y), g1(x,y-1), g1(x-1, y-1)}
(30)
[0107] Otherwise, the expression (16) is replaced by the following
expression (31).
B(x,y)=square root of
[{(dx1(x,y)+dx2(x,y))*.alpha.)}.sup.2+{(dy1(x,y)+dy2-
(x,y))*.beta.)}.sup.2] (31)
[0108] If an position shift of a pattern edge in a x-direction and
that of a pattern edge in a y-direction are independent events with
each other, the expression (31) should bring about a higher
accuracy than the expression (16) does. Compared with the
expression (16), however, the expression (31) causes a problem of
making scale of the hard ware larger. Accordingly, it is advisable
to employ the expression (31) only when the higher accuracy is so
much desirable even if the scale of the hard ware becomes
larger.
[0109] Otherwise, the expression (17) is replaced by the following
expressions (32) to (34).
C(x,y)=((ave1+ave2)/2)*.gamma.+.epsilon. (32)
[0110] where
ave1={f1(x,y)+f1(x+1,y)+f1(x,y+1)+f1(x+1,y+1)}/4 (33)
ave2={g1(x,y)+g1(x-1,y)+g1(x,y-1)+g1(x-1,y-1)}/4 (34)
[0111] Otherwise, instead of the expression (17), the sub CPU 45
prepares in advance a look-up table for a representative gradation
value of quantities such as max1 (refer to the expression (22)),
max2 (refer to the expression (23)), ave1 (refer to the expression
(33)), and ave2 (refer to the expression (34)). Then, the threshold
arithmetic circuit 48 determines C(x,y), following the look-up
table. It would be sometimes difficult to represent the way the
gradation value varies in terms of mathematical functions,
depending on the kind of the image detecting system. In that case,
it is convenient to employ a method using the look-up table.
[0112] Otherwise, the expressions (13) and (14) are replaced by the
following expressions (35) and (36).
thH(x,y)=A(x,y)+square root of {(B(x,y).sup.2+C(x,y).sup.2}
(35)
thL(x,y)-A(x,y)-square root of {(B(x,y).sup.2+C(x,y).sup.2}
(36)
[0113] If an infinitesimal position shift of an individual pattern
edge and a variation in the gradation value are independent events
with each other, the expressions (35) and (36) should bring about a
higher accuracy than the expressions (13) and (14) do. Compared
with the former, however, the latter causes a problem of making
scale of the hard ware larger. Accordingly, it is advisable to
employ the latter only when the higher accuracy is so much
desirable even if the scale of the hard ware becomes larger.
[0114] Second Embodiment
[0115] Described below, using FIG. 8, is a second embodiment of a
method of inspecting a pattern and an apparatus thereof in
connection with the present invention. The present embodiment, as
is the case with the first embodiment, comprises a detecting unit
101, an image fetching unit 102, an image processing unit 103d, and
a general control unit 104 for controlling the whole system. The
detecting unit 101, the image fetching unit 102, and the general
control unit 104 are the same as those in the first embodiment.
Concerning the image processing unit 103d, too, the configuration
and the function are the same as those in the first embodiment by
the time one pixel or less of position shift quantities .delta.x
and .delta.y are calculated in a one pixel or less of position
shift detecting unit 43.
[0116] In a position-shifted image generating unit A 51, a
position-shifted image generating unit B 52, a position-shifted
image generating unit C 53, and a position-shifted image generating
unit D 54, taking as a center the position relationship in which a
detection image f1 and a comparison image g1 to be compared
coincide with each other best in calculation, that is, the position
relationship in which the detection image f1 is shifted by
+.delta.x and +.delta.y and the comparison image g1 is shifted by
-.delta.x and -.delta.y, new images are generated by shifting the
detection image f1 and the comparison image g1 further in a variety
of directions to each other. It is assumed that .alpha. designates
a position shift quantity in a x-direction and .beta. designates a
position shift quantity in a y-direction (.alpha. and .beta. are
real numbers in a range of 0 to 0.
[0117] Namely, generated are f2A (an image generated by shifting f1
by +.alpha. in a x-direction), g2A (an image generated by shifting
g1 by -.alpha. in a x-direction), f2B (an image generated by
shifting f1 by -.alpha. in a x-direction), g2B (an image generated
by shifting g1 by +.alpha. in a x-direction), f2C (an image
generated by shifting f1 by +.beta. in a y-direction), g2C (an
image generated by shifting g1 by -.beta. in a y-direction), f2D
(an image generated by shifting f1 by -.beta. in a y-direction ),
and g2D (an image generated by shifting g1 by +.beta. in a
y-direction ). At that time, since .delta. x, .delta.y, .alpha. and
.beta. are each no integers, it is required to create shifted
images in some way. A variety kinds of methods are known about the
generation of the images. Shown here is a case in which the images
are generated using the interpolation.
f2A(x,y)=f1(x+.delta.x0+.alpha.,y+.delta.y0)=f1(x,y)+(.delta.x0+.alpha.){f-
1(x+1,y)-f1(x,y)}+.delta.y0{f1(x,y+1)-f1(x,y)} (37)
g2A(x,y)=g1(x-.delta.x0-.alpha.,y-.delta.y0)=g1(x,y)+(.delta.x0+.alpha.){g-
1(x-1,y)-g1(x,y)}+.delta.y0{g1(x,y-1)-g1(x,y)} (38)
f2B(x,y)=f1(x+.delta.x0-.alpha.,y+.delta.y0)=f1(x,y)+(.delta.x0-.alpha.){f-
1(x+1,y)-f1(x,y)}+.delta.y0{f1(x,y+1)-f1(x,y)} (39)
g2B(x,y)=g1(x-.delta.x0+.alpha.,y-.delta.y0)=g1(x,y)+(.delta.x0-.alpha.){g-
1(x-1,y)-g1(x,y)}+.delta.y0{g1(x,y-1)-g1(x,y)} (40)
f2C(x,y)=f1(x+.delta.x0,y+.delta.y0+.beta.)=f1(x,y)+.delta.x0{f1(x+1,y)-f1-
(x,y)}+(.delta.y0+.beta.){f1(x,y+1)-f1(x,y)}tm (41)
g2C(x,y)=g1(x-.delta.x0,y-.delta.y0-.beta.)-g1(x,y)+.delta.x0{g1(x-1,y)-g1-
(x,y)}+(.delta.y0+.beta.){g1(x,y-1)-g1(x,y)} (42)
f2D(x,y)=f1(x+.delta.x0,y+.delta.y0-.beta.)=f1(x,y)+.delta.x0{f1(x+1,y)-f1-
(x,y)}+(.delta.y0-.beta.){f1(x,y+1)-f1(x,y)} (43)
g2D(x,y)=g1(x-.delta.x0,y-.delta.y0+.beta.)=g1(x,y)+.delta.x0{g1(x-1,y)-g1-
(x,y)}+(.delta.y0-.beta.){g1(x,y-1)-g1(x,y)} (44)
[0118] Determined by a difference image extracting unit A55, based
on the following expression (45), is sub A, i.e. a difference image
between g2A(x,y) and f2A(x,y) which are outputted from the
pixel-shifted image generating unit A51. Determined by a difference
image extracting unit B56, based on the following expression (46),
is sub B, i.e. a difference image between g2B(x,y) and f2B(x,y)
which are outputted from the pixel-shifted image generating unit
B52. Determined by a difference image extracting unit C57, based on
the following expression (47), is sub C, i.e. a difference image
between g2C(x,y) and f2C(x,y) which are outputted from the
pixel-shifted image generating unit C53. Determined by a difference
image extracting unit D58, based on the following expression (48),
is sub D, i.e. a difference image between g2D(x,y) and f2D(x,y)
which are outputted from the pixel-shifted image generating unit
D54. Namely,
sub A(x,y)=g2A(x,y)-f2A(x,y) (45)
sub B(x,y)=g2B(x,y)-f2B(x,y) (46)
sub C(x,y)=g2C(x,y)-f2C(x,y) (47)
sub D(x,y)=g2D(x,y)-f2D(x,y) (48)
[0119] A maximum/minimum extracting unit 59, by comparing sub A, an
output from the difference image extracting unit A55, sub B, an
output from the difference image extracting unit B56, sub C, an
output from the difference image extracting unit C57, and sub D, an
output from the difference image extracting unit D58, determines
for each pixel a maximum submax(x,y) shown by the following
expression (49) and a minimum submin(x,y) shown by the following
expression (50). Namely,
submax(x,y)=max{sub A(x,y), sub B(x,y), sub C(x,y), sub D(x,y)}
(49)
submin(x,y)=min{sub A(x,y), sub B(x,y), sub C(x,y), sub D(x,y)}
(50)
[0120] Meanwhile, an allowable value arithmetic unit 60 for
calculating an allowable value for variation in a gradation value,
in each of the detection image f1 and the comparison image g1,
determines a representative value (a maximum value, here) of the
gradation value (a value of light and shade) in a local area, and
then, as shown in the expression (51) as a function of the
representative value as is the case with the expression (17),
determines the following allowable value d(x, y) for variation in
the gradation value for each pixel.
d(x,y)=((max1+max2)/2 )*.gamma.+.epsilon. (51)
[0121] (where, .gamma. is a real number greater than zero, and
.epsilon. is an integer greater than zero)
max1=max{f1(x,y), f1(x+1,y), f1(x,y+1), f1(x+1,y+1)} (52)
max2=max{g1(x,y), g1(x-1,y), g1(x,y-1), g1(x-1,y-1)} (53)
[0122] A defect judging circuit 61, adding and subtracting the
above-determined allowable value d(x,y) for variation in the
gradation value to submax(x,y) and from submin(x,y) determined by
the maximum/minimum extracting unit 59, judges a pixel, on which
the signs of the both are opposite, to be an non-defective
candidate and a pixel, on which the signs of the both are same, to
be a defective candidate. Namely, the defect judging circuit 61
judges a pixel at the position(x,y), if the following relation (54)
is satisfied, to be an non-defective candidate, and the pixel at
the position (x,y), if the following relation (54) is not
satisfied, to be a defective candidate. The defect judging circuit
61 outputs, for the non-defective candidate pixel, def(x,y) having
a value of, for example, zero, and outputs, for the defective
candidate pixel, def(x,y) having a value of, for example, one or
more. The expression (54) means that the polarities differ with
each other in the relation between {submax(x,y)+d(x,y)} and
{submin(x,y)-d(x,y)}.
{submax(x,y)+d(x,y)}*{submin(x,y)-d(x,y)}=.ltoreq.0 (54)
[0123] Parameters .alpha. and .beta. in the present second
embodiment have the same meaning as the parameters .alpha. and
.beta. in the first embodiment do. In the first embodiment, in
order to allow an infinitesimal position shift of an individual
pattern edge, B(x,y), i.e. the second term in the threshold values
thH(x,y) and thL(x,y) shown in the above-mentioned expressions (13)
and (14), is adjusted by .alpha. and .beta.. Whereas, in the
present second embodiment, the position is actually shifted by
.+-..alpha. and .+-..beta. between the detection image f1(x,y) and
the comparison image g1(x,y). This brings about an effect of
allowing the infinitesimal position shift of the pattern edges (the
infinitesimal position shift caused by an infinitesimal difference
due to the pattern configuration and the distortion in the
patterns). The reason is explained below, using FIG. 9 and FIG.
10.
[0124] FIG. 9 and FIG. 10 shows the two images to be compared,
paying attention to certain specific pattern edges in the two
images. An edge of the image f is indicated by a full line and an
edge of the image g is indicated by a dotted line. Here, for
simplicity, the gradation value of the image f and that of the
image g are assumed to be equal to each other, and the position is
shifted only in a x-direction.
[0125] FIG. 9(a) shows a case in which there is no infinitesimal
position shift of the pattern edges between the image f and the
image g. Then, if the image g is shifted to the right as shown in
FIG. 9(b), a difference image (g-f) takes a negative value as its
minimum (which corresponds to submin(x,y) shown by the expression
(50)) at the edge part. On the contrary, if the image g is shifted
to the left as shown in FIG. 9(c), the difference image (g-f) takes
a positive value as its maximum (which corresponds to submax(x,y)
shown by the expression (49)) at the edge part. When, from the
beginning, there exists no position shift between the image f and
the image g, no matter how small the quantity by which the image g
is shifted with reference to the image f, polarity (sign) at the
minimum or the maximum of the difference image (g-f) at the edge
is, at the minimum shown in FIG. 9(b), a negative polarity, and at
the maximum shown in FIG. 9(c), a positive polarity.
[0126] On the other hand, FIG. 10(a) shows a case in which there
exists an infinitesimal position shift of the pattern edges. At
this time, if the quantity by which the image g is shifted with
reference to the image f is small compared with the above-mentioned
infinitesimal position shift, as is shown in FIG. 9(b) and FIG.
9(c), whether the image g is shifted to the right or left, the
polarity (sign) at the minimum (which corresponds to submin(x,y)
shown by the expression (50)) or the maximum (which corresponds to
submax(x,y) shown by the expression (49)) of the difference image
(g-f) at the edge is a negative polarity. Generally speaking, when
the image g is shifted in both directions, the polarity (sign) at
the minimum or the maximum is changed, that is,
{submax(x,y)+d(x,y)}*{submin(x,y)-d(x,y)}=0 is satisfied, the pixel
is judged to be a non-defective candidate, and the polarities
(signs) at the minimum and the maximum are the same, that is,
{submax(x,y)+d(x,y)}*{subm- in(x,y)-d(x,y)}.ltoreq.0 is not
satisfied, the pixel is judged to be a defective candidate. In this
situation, accordingly, so as not to be judged to be the defective
candidate even if there exists the infinitesimal position shift of
the pattern edges shown in FIG. 10(a), the shift quantity must be a
certain magnitude or more. In other words, the shift quantity makes
it possible to adjust to what extent the pattern edges should be
allowed. The parameters .alpha. and .beta. in the second embodiment
correspond to this quantity. Namely, .alpha. and .beta. are
parameters which are capable of controlling an allowable value for
the position shift of the pattern edges.
[0127] Also, d(x,y), which is represented by the expression (51) in
the present second embodiment, has a function of allowing an
infinitesimal difference in the gradation value (the value of light
and shade) as is the case with C(x,y) (refer to the expression
(17)) in the first embodiment. In the description of the FIG. 9 and
FIG. 10, the gradation value of the image f and that of the image g
are assumed to be equal to each other. If there is a difference
between the gradation values, there occurs an error in sign of the
difference image after the shift. Consequently, before comparing
the polarities in accordance with the expression (54), d(x,y), i.e.
an allowable value for variation in the gradation value, is added
{submax(x,y)+d(x,y)} or subtracted {submin(x,y)-d(x,y)} so that the
difference between the gradation values exert no influence on the
polarity (sign) of the difference image. Although, d(x,y) is set to
be a summation of a constant .epsilon. and a value obtained by
multiplying a representative value of a gradation value in the
local area (here, a maximum value) by a proportionality constant
.gamma., as explained in the description of the first embodiment,
if the way a gradation value varies is known, a function suitable
therefor should be selected.
[0128] In the present embodiment, the position shift quantity as
the whole small area, which is obtained as the result of the one
pixel or less of position shift detection, is utilized as the
origin coordinate at the time of generating the position-shifted
images. The infinitesimal position shift of the individual pattern
edge is allowed by generating the images the position of which are
shifted in a variety of directions. Moreover, the infinitesimal
difference in gradation value is allowed by calculating the
allowable value for variation in the gradation value for each local
area. Also, as is the case with the first embodiment, the
parameters .alpha., .beta., .gamma. and .epsilon. make it possible
to freely control the position shift and the allowable quantity for
variation in the gradation value
[0129] Modifications of the Second Embodiment
[0130] In the present second embodiment, too, as is the case with
the first embodiment, when the detecting unit 101 detects an image
with a high position accuracy and a position error of the detected
image is less than one pixel, it is possible to omit the pixel unit
of position alignment.
[0131] Also, when the detecting unit 101 detects an image with an
even higher position accuracy and the position error of the
detected image is substantially negligible, it is possible to omit
both the pixel unit of position alignment and the one pixel or less
of position shift detection.
[0132] Also, although the linear interpolation in the expressions
(37) to (44) is employed, there can be a modification in which a
more precise bilinear interpolation is employed. In this case, the
expressions (37) to (44) are replaced by the following expressions
(55) to (62).
f2A(x,y)=f1(x+.delta.x0+.alpha.,y+.delta.y0)=(1-.delta.x0-.alpha.)(1-.delt-
a.y0)f1(x,y)+(.delta.x0+.alpha.)(1-.delta.y0)f1(x+1,y)+(1-.delta.x0-.alpha-
.).delta.y0f1(x,y+1)+(.delta.x0+.alpha.).delta.y0f1(x+1,y+1)
(55)
g2A(x,y)=g1(x-.delta.x0-.alpha.,y-.delta.y0)=(1-.delta.x0-.alpha.)(1-.delt-
a.y0)g1(x,y)+(.delta.x0+.alpha.)(1-.delta.y0)g1(x-1,y)+(1-.delta.x0-.alpha-
.).delta.y0g1(x,y-1)+(.delta.x0+.alpha.).delta.y0g1(x-1,y-1)
(56)
f2B(x,y)=f1(x+.delta.x0-.alpha.,y+.delta.y0)=(1-.delta.x0+.alpha.)(1-.delt-
a.y0)f1(x,y)+(.delta.x0-.alpha.)(1-.delta.y0)f1(x+1,y)+(1-.delta.x0+.alpha-
.).delta.y0f1(x,y+1)+(.delta.x0-.alpha.).delta.y0f1(x+1,y+1)
(57)
g2B(x,y)=g1(x-.delta.x0+.alpha.,y-.delta.y0)=(1-.delta.x0+.alpha.)(1-.delt-
a.y0)g1(x,y)+(.delta.x0-.alpha.)(1-.delta.y0)g1(x-1,y)+(1-.delta.x0+.alpha-
.).delta.y0g1(x,y-1)+(.delta.x0-.alpha.)(.delta.y0g1(x-1,y-1)
(58)
f2C(x,y)=f1(x+.delta.x0,y+.delta.y0+.beta.)=(1-.delta.x0)(1-.delta.y0.beta-
.)f1(x,y)+.delta.x0(1-.delta.y0-.beta.)f1(x+1,y)+(1-.delta.x0)(.delta.y0+.-
beta.)f1(x,y+1)+.delta.x0(.delta.y0+.beta.)f1(x+1,y+1) (59)
g2C(x,y)=g1(x-.delta.x0,y-.delta.y0-.beta.)=(1-.delta.x0)(1-.delta.y0-.bet-
a.)g1(x,y)+.delta.x0(1-.delta.y0-.beta.)g1(x-1,y)+(1-.delta.x0)(.delta.y0+-
.beta.)g1(x,y-1)+.delta.x0(.delta.y0+.beta.)g1(x-1,y-1) (60)
f2D(x,y)=f1(x+.delta.x0,y+.delta.y0-.beta.)=(1-.delta.x0)(1-.delta.y0+.bet-
a.)f1(x,y)+.delta.x0(1-.delta.y0+.beta.)f1(x+1,y)+(1-.delta.x0)(.delta.y0--
.beta.)f1(x,y+1)+.delta.x0(.delta.y0-.beta.)f1(x+1,y+1) (61)
g2D(x,y)=g1(x-.delta.x0,y-.delta.y0+.beta.)=(1-.delta.x0)(1-.delta.y0+.bet-
a.)g1(x,y)+.delta.x0(1-.delta.y0+.beta.)g1(x-1,y)+(1-.delta.x0)(.delta.y0--
.beta.)g1(x,y-1)+.delta.x0(.delta.y0-.beta.)g1(x-1,y-1) (62)
[0133] Also, concerning directions in which an image is shifted,
there can be a modification in which, adding oblique directions,
eight directions are employed instead of the above-described four,
i.e. up-and-down and right-to-left, directions. The shift with
eight directions brings about an advantage of making the allowed
shift quantity more isotropic than the shift with four directions.
In this case, it becomes necessary to provide eight of
position-shifted image generating units and difference extracting
units, respectively, whereas necessary in FIG. 8 are four of the
position-shifted image generating units 51 to 54 and the difference
extracting units 55 to 58, respectively. A magnitude of a shift
quantity with the oblique directions should be equal to that of a
shift quantity with the up-and-down and right-to-left directions,
and thus the expressions should be replaced by the following
expressions (63) to (70).
f2E(x,y)=f1(x+.delta.x0+.alpha./{square root}{square root over (
)}2, y+.delta.y0+.beta./{square root}{square root over ( )}2)
(63)
g2E(x,y)=g1(x-.delta.x0-.alpha./{square root}{square root over (
)}2, y-.delta.y0-.beta./{square root}{square root over ( )}2)
(64)
f2F(x,y)=f1(x+.delta.x0+.alpha./{square root}{square root over (
)}2, y+.delta.y0-.beta./{square root}{square root over ( )}2)
(65)
g2F(x,y)=g1(x-.delta.x0-.alpha./{square root}{square root over (
)}2, y-.delta.y0+.beta./{square root}{square root over ( )}2)
(66)
f2G(x,y)=f1(x+.delta.x0-.alpha./{square root}{square root over (
)}2, y+.delta.y0+.beta./{square root}{square root over ( )}2)
(67)
g2G(x,y)=g1(x-.delta.x0+.alpha./{square root}{square root over (
)}2, y-.delta.y0-.beta./{square root}{square root over ( )}2)
(68)
f2H(x,y)=f1(x+.delta.x0-.alpha./{square root}{square root over (
)}2, y+.delta.y0-.beta./{square root}{square root over ( )}2)
(69)
g2H(x,y)=g1(x-.delta.x0+.alpha./{square root}{square root over (
)}2, y.sym..delta.y0+.beta./{square root}{square root over ( )}2)
(70)
[0134] Regarding a method of interpolation in the oblique
directions, too, possible area linear interpolation, a bilinear
interpolation, and so on. Also, there can be a modification in
which, as is the case with the fourth modification of the first
embodiment, the following expressions (71) to (73) are employed
instead of the expression (51).
d(x,y)=((ave1+ave2)/2)*.gamma.+.epsilon. (71)
[0135] where
ave1={f1(x,y)+f1(x+1,y)+f1(x,y+1)+f1(x+1,y+1)}/4 (72)
ave2={g1(x,y)+g1(x-1,y)+g1(x,y-1)+g1(x-1,y+1)}/4 (73)
[0136] Otherwise, there can be a modification in which, instead of
the expression (51), the sub CPU 45 prepares in advance a look-up
table for a representative gradation value of quantities such as
maxi (refer to the expression (52)), max2 (refer to the expression
(53)), ave1 (refer to the expression (72)), and ave2 (refer to the
expression (73), and then the allowable value arithmetic unit 60
determines d(x,y) in accordance with the look-up table.
[0137] Modifications common to First Embodiment and Second
Embodiment A method of comparing two images derived from an
identical object is shown in the above-described first and second
embodiments. It is evident, however, that the content in the image
processing unit can be embodied in much the same way even when
comparing with an image obtained by detecting anther object and
storing it in advance or with an image generated from design
data.
[0138] Also, a case of apparatuses employing an electronic optical
detecting means is described in the above-described first and
second embodiments. It is needless to say, however, that the
content in the present invention can be embodied in much the same
way even when employing any kind of detecting means such as the
optical detecting means shown in FIG. 4.
[0139] Namely, FIG. 4 shows a brief configuration of an apparatus
of inspecting a pattern in which an optical detecting means (a
detecting unit) 101' is employed. The detecting unit 101' comprises
a stage 2 for mounting an object to be inspected 100 such as a
semiconductor wafer and moving it in a x-direction and a
y-direction, an light source 3, an illuminating optical system 4
for gathering a light beam emitted from the light source 3, an
objective lens 5 for illuminating an illuminating light beam
gathered by the illuminating optical system 4 to the object to be
inspected 100 and focusing an optical image reflected from the
object to be inspected 100, and a one-dimensional image sensor 6,
i.e. an embodiment of a photoelectric converter for receiving an
optical image focused by a detecting optical system including the
objective lens 5 and converting it into an image signal
corresponding to the illumination. The image signal detected by the
one-dimensional image sensor 6 in the detecting unit 101' is
inputted into an image inputting unit 102'. The image inputting
unit 102 has an A/D converter 39 and an image memory unit 41' for
storing a digital image signal, which has a gradation value(a value
of light and shade) obtained from the A/D converter 39, so as to
create a comparison image g0 from the digital image signal.
Naturally, it is allowable that the image inputting unit 102' is
provided with a preprocessing circuit 40 for a shading amendment, a
dark level amendment, a filtering process, and so on. An image
processing unit 103a, the configuration of which is the same as the
configuration shown in FIG. 1, is able to perform a judgement,
based on the same image processing, as to whether a defective
candidate or a non-defective candidate, and a calculation of a
characteristic quantity about the defective candidate. The image
processing unit 103a, however, is provided with a comparison image
fetching unit 78 for fetching the comparison image from the image
memory unit 41'. In this way, the delay circuit 41 shown in FIG. 1
may be replaced by the image memory 41' and the comparison image
fetching unit 78.
[0140] The present invention exhibits an effect of making it
possible to decrease the number of false information, which is
caused by mismatches such as an infinitesimal difference in pattern
configuration, a difference in gradation value, distortion of a
pattern, and a position shift attributed to an object to be
inspected and an image detecting system, and to detect a more
microscopic defect or a candidate for a more microscopic
defect.
[0141] The present invention also exhibits an effect of, when a
pattern formed on an object to be inspected is inspected by means
of an electron microscope, making it possible to decrease the
number of false information, which is caused by mismatches such as
an infinitesimal difference in pattern configuration, a difference
in gradation value, distortion of the pattern, and a position shift
attributed to the object to be inspected and an image detecting
system, and to detect a more microscopic defect or a candidate for
a more microscopic defect.
[0142] The present invention also exhibits an effect of making it
possible to obtain an image signal having a stable gradation value
(a value of light and shade) from an inspection through an electron
microscope of a pattern formed on an object to be inspected, and
thus to stably detect a more microscopic defect or a candidate for
a more microscopic defect.
* * * * *