System and method for simulating an aerial image
First Claim
1. A method for generating a simulated aerial image, comprising:
- forming a reference aerial image of a first mask for an optical system;
capturing and processing the reference aerial image so as to generate a set of expansion functions representative of aberrations in the optical system; and
computing the simulated aerial image of a second mask for use in the optical system by applying the expansion functions to a design of the second mask, wherein the first mask comprises a pseudo-noise pattern characterized by a transmission function g that approximates a condition;
∫
∫
g({right arrow over (x)}−
{right arrow over (z)}1)●
g({right arrow over (x)}−
{right arrow over (z)}2) ●
g({right arrow over (x)}−
{right arrow over (z)}3)●
g({right arrow over (x)}−
{right arrow over (z)}4)d{right arrow over (x)}=Gδ
({right arrow over (z)}1−
{right arrow over (z)}3,{right arrow over (z)}2−
{right arrow over (z)}4)wherein;
G is a constant, {right arrow over (z)}j {j=1, 2, 3, 4} are arbitrary vectors. {right arrow over (x)} is a vector in a mask plane in the optical system, and δ
is a function of {right arrow over (z)}j {j=1, 2, 3, 4}.
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Abstract
Simulated aerial images for an optical system are made by forming a reference aerial image of a first mask used in connection with the optical system, and then capturing and processing the reference aerial image to generate a set of expansion functions representative of the optical system. The expansion functions account for aberrations and misalignment of the optical system, as well as any aberrations or other defects of a camera therein. The expansion functions are then used to compute simulated aerial images of other masks projected by the optical system. Thus, the expansion functions implicitly represent a calibration of the optical system for purposes of aerial image simulation, obviating the need for direct measurement of the actual aberrations and misalignment. Hence, a simulated aerial image of a second mask for the optical system can be computed by applying the expansion functions to a design of the second mask.
13 Citations
21 Claims
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1. A method for generating a simulated aerial image, comprising:
- forming a reference aerial image of a first mask for an optical system;
capturing and processing the reference aerial image so as to generate a set of expansion functions representative of aberrations in the optical system; and
computing the simulated aerial image of a second mask for use in the optical system by applying the expansion functions to a design of the second mask, wherein the first mask comprises a pseudo-noise pattern characterized by a transmission function g that approximates a condition;
∫
∫
g({right arrow over (x)}−
{right arrow over (z)}1)●
g({right arrow over (x)}−
{right arrow over (z)}2) ●
g({right arrow over (x)}−
{right arrow over (z)}3)●
g({right arrow over (x)}−
{right arrow over (z)}4)d{right arrow over (x)}=Gδ
({right arrow over (z)}1−
{right arrow over (z)}3,{right arrow over (z)}2−
{right arrow over (z)}4)wherein;
G is a constant, {right arrow over (z)}j {j=1, 2, 3, 4} are arbitrary vectors. {right arrow over (x)} is a vector in a mask plane in the optical system, and δ
is a function of {right arrow over (z)}j {j=1, 2, 3, 4}.- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
- forming a reference aerial image of a first mask for an optical system;
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10. Apparatus for modeling an optical system, comprising:
- a camera, which is adapted to capture a reference aerial image of a first mask for the optical system, which image is formed using the optical system; and
an image processor, which is adapted to process the reference aerial image so as to generate a set of expansion functions representative of aberrations in the optical system, and to compute a simulated aerial image of a second mask for use in the optical system by applying the expansion functions to a design of the second mask, wherein the first mask comprises a pseudo-noise pattern characterized by a transmission function g that approximates a condition;
∫
∫
g({right arrow over (x)}−
{right arrow over (z)}1)●
g({right arrow over (x)}−
{right arrow over (z)}2)●
g({right arrow over (x)}−
{right arrow over (z)}3)●
g({right arrow over (x)}−
{right arrow over (z)}4)d{right arrow over (x)}=Gδ
({right arrow over (z)}1−
{right arrow over (z)}3,{right arrow over (z)}2−
{right arrow over (z)}4)wherein;
G is a constant, {right arrow over (z)}j {j=1, 2, 3, 4} are arbitrary vectors, {right arrow over (x)}j is a vector in a mask plane in the optical system, and δ
is a function of {right arrow over (z)}j {j=1, 2, 3, 4}.- View Dependent Claims (11, 12, 13, 14, 15, 16, 17, 18)
- a camera, which is adapted to capture a reference aerial image of a first mask for the optical system, which image is formed using the optical system; and
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19. Apparatus for mask inspection, comprising:
- an optical system, which is adapted to form aerial images of masks, the aerial images comprising a reference aerial image of a first mask for use in the optical system and an actual aerial image of a second mask for use in the optical system;
a camera, which is adapted to capture the aerial images formed by the optical system; and
an image processor, which is adapted to process the reference aerial image so as to generate a set of expansion functions representative of aberrations in the optical system, and to compute a simulated aerial image of a second mask by applying the expansion functions to a design of the second mask, and to compare the actual aerial image to the simulated aerial image so as to evaluate the second mask, wherein the first mask comprises a pseudo-noise pattern characterized by a transmission function g that approximates a condition;
∫
∫
g({right arrow over (x)}−
{right arrow over (z)}1)●
g({right arrow over (x)}−
{right arrow over (z)}2)●
g({right arrow over (x)}−
{right arrow over (z)}3)●
g({right arrow over (x)}−
{right arrow over (z)}4)d{right arrow over (x)}=Gδ
({right arrow over (z)}1−
{right arrow over (z)}3,{right arrow over (z)}2−
{right arrow over (z)}4)wherein;
G is a constant, {right arrow over (z)}j {j=1, 2, 3, 4} are arbitrary vectors, {right arrow over (x)} is a vector in a mask plane in the optical system, and δ
is a function of {right arrow over (z)}j {j=1, 2, 3, 4}.- View Dependent Claims (20)
- an optical system, which is adapted to form aerial images of masks, the aerial images comprising a reference aerial image of a first mask for use in the optical system and an actual aerial image of a second mask for use in the optical system;
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21. A computer software product for modeling an optical system, the product comprising a computer-readable medium, in which program instructions are stored, which instructions, when read by a computer, cause the computer to process a reference aerial image of a first mask for use in the optical system, which image is formed using the optical system, so as to generate a set of expansion functions representative of aberrations in the optical system, and to compute a simulated aerial image of a second mask for use in the optical system by applying the expansion functions to a design of the second mask, wherein the first mask comprises a pseudo-noise pattern characterized by a transmission function g that approximates a condition:
-
∫
∫
g({right arrow over (x)}−
{right arrow over (z)}1)●
g({right arrow over (x)}−
{right arrow over (z)}2)●
g({right arrow over (x)}−
{right arrow over (z)}3)●
g({right arrow over (x)}−
{right arrow over (z)}4)d{right arrow over (x)}=Gδ
({right arrow over (z)}1−
{right arrow over (z)}3,{right arrow over (z)}2−
{right arrow over (z)}4)wherein;
G is a constant, {right arrow over (z)}j {j=1, 2, 3, 4} are arbitrary vectors, {right arrow over (x)} is a vector in a mask plane in the optical system, and δ
is a function of {right arrow over (z)}j {j=1, 2, 3, 4}.
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Specification