Method of OPC modeling
In a method of optical proximity correction (OPC) modeling, a resist image (RI) model is generated from an aerial image (AI) of a pattern. A light intensity of a portion having a level lower than a truncation level is replaced with the truncation level in an image profile of the RI model. The image profile is smoothed to remove a sharp point in the image profile. A Laplacian kernel is applied to the image profile to generate a contour image profile. A portion of the contour image profile having a value lower than a given level is truncated. A radius of curvature kernel is applied to the contour image profile. A reciprocal number of the radius of curvature is applied to the RI model.
1. An optical proximity correction (OPC) method comprising:
generating a resist image (RI) model from an aerial image (AI) of a pattern;
replacing a light intensity of a portion of an image profile of the RI model, the portion having a level lower than a truncation level, with the truncation level;
smoothing the image profile such that a sharp point in the image profile is removed;
applying a Laplacian kernel to the smoothed image profile to generate a contour image profile;
truncating a portion of the contour image profile having a value lower than a set level;
applying a radius of curvature kernel to the contour image profile; and
applying a reciprocal number of the radius of curvature to the RI model.
2. The method of claim 1 , wherein replacing the light intensity of the portion having the level lower than the truncation level includes using a truncation kernel represented by
f ( x )=max( x , truncation level)
wherein x is the light intensity.
3. The method of claim 2 , wherein smoothing the image profile includes using a rectification kernel represented by
f
(
x
′
)
=
ln
(
1
+
e
kx
′
)
k
wherein x′ is a result after the application of the truncation kernel and k is a constant.
4. The method of claim 3 , wherein the Laplacian kernel is represented by
Δ
f
=
∇
2
f
=
∇
·
∇
f
=
∑
i
=
1
n
∂
2
f
∂
x
i
2
wherein f is a result after the application of the rectification kernel.
5. The method of claim 4 , wherein the set level is zero such that truncating the portion of the contour image profile includes truncating a portion having a negative value after the application of the Laplacian kernel.
6. The method of claim 1 , wherein the radius of kernel is represented by
1
R
=
-
(
-
F
y
F
x
)
(
F
xx
F
xy
F
yx
F
yy
)
(
-
F
y
F
x
)
(
F
x
2
+
F
y
2
)
3
/
2
=
❘
"\[LeftBracketingBar]"
F
y
2
F
xx
-
2
F
x
F
y
F
xy
+
F
x
2
F
yy
(
F
x
2
+
F
y
2
)
3
/
2
❘
"\[RightBracketingBar]"
where
F
x
=
∂
x
f
(
x
,
y
)
,
F
xx
=
∂
xx
f
(
x
,
y
)
=
∂
x
2
f
(
x
,
y
)
wherein x and y are plane coordinates, and f(x, y) is a result after the application of the Laplacian kernel at each position.
7. The method of claim 1 , wherein the pattern includes a shape of a line extending in a direction, and
wherein the reciprocal number of the radius of curvature is substantially zero at a sidewall of the line and is greater than zero at an end of line (EOL) of the line.
8. The method of claim 1 , wherein the pattern includes a first line and a second line each extending in a first direction, and a third line extending in a second direction such that the third line is connected to the first and second lines, and
wherein the reciprocal number is substantially zero at a sidewall of each of the first and second lines and is greater than zero at a portion of the third line contacting at least one of the first line or the second line.
9. An optical proximity correction (OPC) method comprising:
generating a resist image (RI) model from an aerial image (AI) of a pattern, the pattern including, at least, a first line and a second line each extending in a first direction and a third line extending in a second direction such that the third line is connected to the first and second lines;
replacing a light intensity of a portion of an image profile of the RI model, the portion having a level lower than a truncation level, with the truncation level;
smoothing the image profile such that a sharp point in the image profile is removed;
applying a Laplacian kernel to the smoothed image profile to generate a contour image profile;
truncating a portion of the contour image profile having a value lower than a set level;
applying a radius of curvature kernel to the contour image profile; and
applying a reciprocal number of the radius of curvature to the RI model.
10. The method of claim 9 , wherein replacing the light intensity of the portion having the level lower than the truncation level includes using a truncation kernel represented by
f ( x )=max( x , truncation level)
wherein x is the light intensity.
11. The method of claim 10 , wherein smoothing the image profile includes using a rectification kernel represented by
f
(
x
′
)
=
ln
(
1
+
e
kx
′
)
k
wherein x′ is a result after the application of the truncation kernel, and k is a constant.
12. The method of claim 11 , wherein the Laplacian kernel is represented by
Δ
f
=
∇
2
f
=
∇
·
∇
f
=
∑
i
=
1
n
∂
2
f
∂
x
i
2
wherein f is a result after the application of the rectification kernel.
13. The method of claim 12 , wherein the set level is zero such that truncating the portion of the contour image profile includes truncating a portion having a negative value after the application of the Laplacian kernel.
14. The method of claim 9 , wherein the radius of kernel is represented by,
1
R
=
-
(
-
F
y
F
x
)
(
F
xx
F
xy
F
yx
F
yy
)
(
-
F
y
F
x
)
(
F
x
2
+
F
y
2
)
3
/
2
=
❘
"\[LeftBracketingBar]"
F
y
2
F
xx
-
2
F
x
F
y
F
xy
+
F
x
2
F
yy
(
F
x
2
+
F
y
2
)
3
/
2
❘
"\[RightBracketingBar]"
where
F
x
=
∂
x
f
(
x
,
y
)
,
F
xx
=
∂
xx
f
(
x
,
y
)
=
∂
x
2
f
(
x
,
y
)
x and y are plane coordinates, and f(x, y) is a result after the application of the Laplacian kernel at each position.
15. The method of claim 9 , wherein the reciprocal number is substantially zero at a sidewall of each of the first and second lines and is greater than zero at a portion of the third line contacting at least one of the first line or the second line.
16. The method of claim 9 , wherein the reciprocal number of the radius of curvature is zero or close to zero at a sidewall of each of the first and second lines and is greater than zero at an end of line (EOL) of each of the first and second lines.
17. An OPC method comprising:
generating a resist image (RI) model from an aerial image (AI) of a pattern;
replacing a light intensity of a portion of an image profile of the RI model, the portion having a level lower than a truncation level, with the truncation level;
applying a Laplacian kernel to the image profile to generate a contour image profile;
truncating a portion of the contour image profile having a value lower than a set level;
applying a radius of curvature kernel to the contour image profile; and
applying a reciprocal number of the radius of curvature to the RI model.
18. The method of claim 17 , further comprising:
after replacing the light intensity of the portion having the level lower than the truncation level, smoothing the image profile such that a sharp point in the image profile is removed.
19. The method of claim 18 , wherein smoothing the image profile to remove the sharp point in the image profile includes using a rectification kernel represented by
f
(
x
′
)
=
ln
(
1
+
e
kx
′
)
k
wherein x′ is a result after the application of the truncation kernel and k is a constant.
20. The method of claim 17 , wherein replacing the light intensity of the portion having the level lower than the truncation level includes using a truncation kernel represented by
f ( x )=max( x , truncation level)
wherein x is a light intensity.