Source and mask optimization by changing intensity and shape of the illumination source
An illumination source is optimized by changing the intensity and shape of the illumination source to form an image in the image plane that maximizes the minimum ILS at user selected fragmentation points while forcing the intensity at the fragmentation points to be within a small intensity range. An optimum mask may be determined by changing the magnitude and phase of the diffraction orders to form an image in the image plane that maximizes the minimum ILS at user selected fragmentation points while forcing the intensity at the fragmentation points to be within a small intensity range. Primitive rectangles having a size set to a minimum feature size of a mask maker are assigned to the located minimum and maximum transmission areas ad centered at a desired location. The edges of the primitive rectangle are varied to match optimal diffraction orders O(m,n). The optimal CPL mask O CPL (x,y) is then formed.
1. A method for determining an optimal mask comprising the steps of:
identifying a predetermined range of illumination intensity values based on specifications of an illumination system for illuminating the optimal mask;
determining optimum diffraction orders;
obtaining an optimal transmission mask based on the optimum diffraction orders based on the identified predetermined range; and
determining an optimal mask based on the optimal transmission mask,
wherein the optimum diffraction orders are determined by determining a magnitude and phase of diffraction orders which form an image in an image plane of the illumination system which maximizes the minimum illumination log slope at user selected fragmentation points of the optimal mask while forcing an intensity of illumination at the fragmentation points to be within the predetermined range.
2. The method of claim 1 , wherein the step of obtaining the optimal transmission mask includes a step of determining a number of horizontal diffraction orders of the optimum diffraction orders, wherein the number of horizontal diffraction orders is determined according to the equation:
m
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where m is the number of horizontal diffraction orders;
P x is the pitch of a repetitive cell in the x direction of the optimal mask;
λ is a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.
3. The method of claim 1 , wherein the step of obtaining the optimal transmission mask includes a step of determining a number of vertical diffraction orders of the optimum diffraction orders, wherein the number of vertical diffraction orders is determined according to the equation
n
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where n is the number of vertical diffraction orders;
P x is the pitch of a repetitive cell in the y direction of the optimal mask;
λ is a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.
4. The method of claim 1 , wherein the step of determining optimum diffraction orders determines optimum diffraction orders in the spatial frequency domain.
5. The method of claim 1 , wherein the step of determining an optimal mask comprises the steps of:
locating areas of maximum transmission and minimum transmission;
assigning a primitive area as an area centered on an area of maximum transmission or minimum transmission;
varying edges of the primitive area to match the optimum diffraction orders,
wherein the primitive area has a minimum size which is substantially equal to a minimum feature size of the optimal mask.
6. A method of optimizing a placement of transmission and phase shifting features on a mask comprising the steps of:
obtaining optimal mask transmission characteristics based on optimum diffraction orders of the mask;
locating areas of maximum transmission and minimum transmission through the mask based on the obtained optimal mask transmission characteristics;
assigning a primitive area in the mask as an area centered on one of the areas of maximum transmission and minimum transmission;
varying edges of primitive area to match the optimum diffraction orders, wherein the primitive area has a minimum size which is substantially equal to a minimum feature size of the mask.
7. The method of claim 6 , wherein the step of obtaining optimal mask transmission characteristics includes a step of determining a number of horizontal diffraction orders of an optimum mask to be illuminated by an identified illumination system, wherein the number of horizontal diffraction orders is determined according to the equation:
m
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where m is the number of horizontal diffraction orders;
P x is the pitch of the repetitive cell in the mask in the x direction;
λ is a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of the projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.
8. The method of claim 6 wherein the step of obtaining optimal mask transmission characteristics includes a step of determining a number of vertical diffraction orders of an optimum mask to be illuminated by an identified illumination system, wherein the number of vertical diffraction orders is determined according to the equation
n
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where n is the number of vertical diffraction orders;
P x is the pitch of the repetitive cell in the mask in the y direction;
λ is a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of the projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.
9. The method of claim 6 , wherein the mask is a CPL mask.
10. A computer readable medium containing instructions stored therein which, when executed by a computer, causes the computer to perform a method for determining an optimal mask comprising the steps of:
identifying a predetermined range of illumination intensity values based on specifications of an illumination system for illuminating the optimal mask;
determining optimum diffraction orders;
obtaining an optimal transmission mask based on the optimum diffraction orders based on the identified predetermined range; and
determining an optimal mask based on the optimal transmission mask,
wherein the optimum diffraction orders are determined by determining a magnitude and phase of diffraction orders which form an image in an image plane of the illumination system which maximizes the minimum illumination log slope at user selected fragmentation points of the optimal mask while forcing an intensity of illumination at the fragmentation points to be within the predetermined range.
11. The computer readable medium of claim 10 , wherein the step of obtaining the optimal transmission mask includes a step of determining a number of horizontal diffraction orders of the optimum diffraction orders, wherein the number of horizontal diffraction orders is determined according to the equation:
m
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where m is the number of horizontal diffraction orders;
P x is the pitch of the repetitive cell in the x direction of the optimal mask;
λ is a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of the projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.
12. The computer readable medium of claim 10 , wherein the step of obtaining the optimal transmission mask includes a step of determining a number of vertical diffraction orders of the optimum diffraction orders, wherein the number of vertical diffraction orders is determined according to the equation
n
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where n is the number of vertical diffraction orders;
P x is the pitch of a repetitive cell in the y direction of the optimal mask;
λ is a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of the projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.
13. The computer readable medium of claim 10 , wherein the step of determining optimum diffraction orders determines optimum diffraction orders in the spatial frequency domain.
14. The computer readable medium of claim 10 , wherein the step of determining an optimal mask comprises the steps of:
locating areas of maximum transmission and minimum transmission;
assigning a primitive area as an area centered on an area of maximum transmission or minimum transmission;
varying edges of the primitive area to match the optimum diffraction orders,
wherein the primitive area has a minimum size which is substantially equal to a minimum feature size of the optimal mask.
15. A computer readable medium containing instructions stored therein which, when executed by a computer, causes the computer to perform a method of optimizing a placement of transmission and phase shifting features on a mask comprising the steps of:
obtaining optimal mask transmission characteristics based on optimum diffraction orders of the mask;
locating areas of maximum transmission and minimum transmission through the mask based on the obtained optimal mask transmission characteristics;
assigning a primitive area in the mask as an area centered on one of the areas of maximum transmission and minimum transmission;
varying edges of the primitive area to match the optimum diffraction orders, wherein the primitive area has a minimum size which is substantially equal to a minimum feature size of the mask.
16. The computer readable medium of claim 15 , wherein the mask is a CPL mask.
17. The computer readable medium of claim 15 , wherein the step of obtaining optimal mask transmission characteristics includes a step of determining a number of horizontal diffraction orders of an optimum mask to be illuminated by an identified illumination system, wherein the number of horizontal diffraction orders is determined according to the equation:
m
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where m is the number of horizontal diffraction orders;
P x is the pitch of the repetitive cell in the mask in the x direction;
λ is a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.
18. The computer readable medium of claim 15 , wherein the step of obtaining optimal mask transmission characteristics includes a step of determining a number of vertical diffraction orders of an optimum mask to be illuminated by an identified illumination system, wherein the number of vertical diffraction orders is determined according to the equation
n
=
2
floor
[
P
x
(
σ
max
+
1
)
NA
λ
]
+
1
where n is the number of vertical diffraction orders;
P x is the pitch of the repetitive cell in the mask in the y direction;
λis a wavelength of an illumination source of the illumination system;
NA is a numerical aperture of projection optics of the illumination system; and
σ max is a radial extent of the distribution of a beam of light from the illumination source.