Horizontal development bias in negative tone development of photoresist
View Patent ↗Aspects of the disclosed techniques relate to techniques for resist simulation in lithography. Local minimal light intensity values are determined for a plurality of sample points in boundary regions of an aerial image of a feature to be printed on a resist coating, wherein each of the local minimal light intensity values represents a minimum light intensity value for an area surrounding one of the plurality of sample points. Based on the local minimal light intensity values, horizontal development bias values for the plurality of sample points are then determined. Finally, resist contour data of the feature are determined based at least on the horizontal development bias values.
1. A method, executed by at least one processor of a computer, comprising:
determining local minimal light intensity values for a plurality of sample points in boundary regions of an aerial image of a feature of an electronic design to be printed on a resist coating, wherein each of the local minimal light intensity values represents a minimum light intensity value for an area surrounding one of the plurality of sample points;
determining horizontal development bias values for the plurality of sample points based on the local minimal light intensity values; and
computing, as part of a process for verifying printability of the feature or for modifying the feature, resist contour data of the feature based at least on the horizontal development bias values.
2. The method recited in claim 1 , wherein the local minimal light intensity values are determined according to
I
m
(
x
,
y
)
=
1
2
*
b
*
(
b
2
-
(
(
I
-
b
)
2
⊗
G
s
)
(
x
,
y
)
)
,
where
G
s
(
x
,
y
)
=
1
π
s
2
exp
(
-
x
2
+
y
2
s
2
)
is a Gaussian kernel with diffusion length s, I −b (x, y) is a result of the “minus” neutralization with the neutralization constant b, and x, y are coordinates, and wherein the horizontal development bias values are determined according to
H
(
x
,
y
)
=
c
*
a
2
+
(
I
m
(
x
,
y
)
)
2
*
(
∂
I
(
x
,
y
)
∂
x
)
2
+
(
∂
I
(
x
,
y
)
∂
y
)
2
.
where c is a linear coefficient, a is a constant, and I(x,y) is light intensity at (x,y).
3. The method recited in claim 1 , wherein the horizontal development bias values are determined according to
Δ x≈R min*[ t dev −h
where Imin represents the local minimal light intensity values, R max is dissolution rate of fully exposed resist, R min is dissolution rate of unexposed resist, t dev is horizontal development time, h is depth, and γ and r 0 are constants.
4. A non-transitory processor-readable medium storing processor-executable instructions for causing one or more processors to perform a method, the method comprising:
determining local minimal light intensity values for a plurality of sample points in boundary regions of an aerial image of a feature of an electronic design to be printed on a resist coating, wherein each of the local minimal light intensity values represents a minimum light intensity value for an area surrounding one of the plurality of sample points;
determining horizontal development bias values for the plurality of sample points based on the local minimal light intensity values; and
computing, as part of a process for verifying printability of the feature or for modifying the feature, resist contour data of the feature based at least on the horizontal development bias values.
5. The non-transitory processor-readable medium recited in claim 4 , wherein the local minimal light intensity values are determined according to
I
m
(
x
,
y
)
=
1
2
*
b
*
(
b
2
-
(
(
I
-
b
)
2
⊗
G
s
)
(
x
,
y
)
)
,
where
G
s
(
x
,
y
)
=
1
π
s
2
exp
(
-
x
2
+
y
2
s
2
)
is a Gaussian kernel with diffusion length s, I −b (x, y) is a result of the “minus” neutralization with the neutralization constant b, and x, y are coordinates,
and wherein the horizontal development bias values are determined according to
H
(
x
,
y
)
=
c
*
a
2
+
(
I
m
(
x
,
y
)
)
2
*
(
∂
I
(
x
,
y
)
∂
x
)
2
+
(
∂
I
(
x
,
y
)
∂
y
)
2
where c is a linear coefficient, a is a constant, and I(x,y) is light intensity at (x,y).
6. The non-transitory processor-readable medium recited in claim 4 , wherein the horizontal development bias values are determined according to
Δ x≈R min*[ t dev −h
where Imin represents the local minimal light intensity values, R max is dissolution rate of fully exposed resist, R min is dissolution rate of unexposed resist, t dev is horizontal development time, h is depth, and γ and r 0 are constants.
7. A system, comprising:
a local minimum light intensity determination unit configured to determine local minimal light intensity values for a plurality of sample points in boundary regions of an aerial image of a feature of an electronic design to be printed on a resist coating, wherein each of the local minimal light intensity values represents a minimum light intensity value for an area surrounding one of the plurality of sample points;
a horizontal development bias values determination unit configured to determine horizontal development bias values for the plurality of sample points based on the local minimal light intensity values; and
a resist contour simulation unit configured to compute, as part of a process for verifying printability of the feature or for modifying the feature, resist contour data of the feature based at least on the horizontal development bias values.
8. The system recited in claim 7 , wherein the local minimal light intensity values are determined according to
I
m
(
x
,
y
)
=
1
2
*
b
*
(
b
2
-
(
(
I
-
b
)
2
⊗
G
s
)
(
x
,
y
)
)
,
where
G
s
(
x
,
y
)
=
1
π
s
2
exp
(
-
x
2
+
y
2
s
2
)
is a Gaussian kernel with diffusion length s, I −b (x, y) is a result of the “minus” neutralization with the neutralization constant b, and x, y are coordinates,
and wherein the horizontal development bias values are determined according to
H
(
x
,
y
)
=
c
*
a
2
+
(
I
m
(
x
,
y
)
)
2
*
(
∂
I
(
x
,
y
)
∂
x
)
2
+
(
∂
I
(
x
,
y
)
∂
y
)
2
where c is a linear coefficient, a is a constant, and I(x,y) is light intensity at (x,y).
9. The system recited in claim 7 , wherein the horizontal development bias values are determined according to
Δ x≈R min*[ t dev −h
where Imin represents the local minimal light intensity values, R max is dissolution rate of fully exposed resist, R min is dissolution rate of unexposed resist, t dev is horizontal development time, h is depth, and γ and r 0 are constants.