Constrained Optimization Of Lithographic Source Intensities Under Contingent Requirements
First Claim
1. A method for illuminating a mask to project a desired image pattern into a photoactive material, the method comprising:
- receiving an image pattern;
determining a relationship between at least one source pixel in a set of source pixels to at least one desired intensity at at least one point in the image pattern;
imposing at least one linear constraint on a set of intensity values based on at least one contingent intensity condition, where the at least one contingent intensity condition comprises at least one integer variable specifying at least one contingent constraint;
determining values of the set of intensity values in accordance with the at least one linear constraint, using a constrained optimization algorithm; and
outputting the set of intensity values, where the set of intensity values represents intensities for the set of source pixels.
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Abstract
A method for illuminating a mask to project a desired image pattern into a photoactive material is described. The method includes receiving an image pattern. Determining a relationship between source pixels in a set of source pixels to desired intensities at one or more points in the image pattern is performed. Linear constraints are imposed on a set of intensity values based on one or more contingent intensity condition. The contingent intensity conditions include integer variables specifying contingent constraints. The method includes determining values of the set of intensity values in accordance with the linear constraints, using a constrained optimization algorithm. The set of intensity values represents intensities of a set of source pixels. The set of intensity values are output. Apparatus and computer readable storage media are also described.
18 Citations
20 Claims
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1. A method for illuminating a mask to project a desired image pattern into a photoactive material, the method comprising:
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receiving an image pattern; determining a relationship between at least one source pixel in a set of source pixels to at least one desired intensity at at least one point in the image pattern; imposing at least one linear constraint on a set of intensity values based on at least one contingent intensity condition, where the at least one contingent intensity condition comprises at least one integer variable specifying at least one contingent constraint; determining values of the set of intensity values in accordance with the at least one linear constraint, using a constrained optimization algorithm; and outputting the set of intensity values, where the set of intensity values represents intensities for the set of source pixels. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. An apparatus for illuminating a mask to project a desired image pattern into a photoactive material, the apparatus comprising:
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a receiver configured to receive an image pattern; a controller configured to determine a relationship between at least one source pixel in a set of source pixels to at least one desired intensity at at least one point in the image pattern, to impose at least one linear constraint on a set of intensity values based on at least one contingent intensity condition, where the at least one contingent intensity condition comprises at least one integer variable specifying at least one contingent constraint, and to determine values of the set of intensity values in accordance with the at least one linear constraint, using a constrained optimization algorithm; and an output configured to output the set of intensity values, where the set of intensity values represents intensities for the set of source pixels. - View Dependent Claims (10, 11, 12, 13, 14)
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15. A computer readable storage medium having computer readable program code embodied therewith for illuminating a mask to project a desired image pattern into a photoactive material, the computer readable program code comprising instructions comprising:
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receiving an image pattern; determining a relationship between at least one source pixel in a set of source pixels to at least one desired intensity at at least one point in the image pattern; imposing at least one linear constraint on a set of intensity values based on at least one contingent intensity condition, where the at least one contingent intensity condition comprises at least one integer variable specifying at least one contingent constraint; determining values of the set of intensity values in accordance with the at least one linear constraint, using a constrained optimization algorithm; and outputting the set of intensity values, where the set of intensity values represents intensities for the set of source pixels. - View Dependent Claims (16, 17, 18)
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19. An apparatus for illuminating a mask to project a desired image pattern into a photoactive material, the apparatus comprising:
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means for receiving an image pattern; means for determining a relationship between at least one source pixel in a set of source pixels to at least one desired intensity at at least one point in the image pattern; means for imposing at least one linear constraint on a set of intensity values based on at least one contingent intensity condition, where the at least one contingent intensity condition comprises at least one integer variable specifying at least one contingent constraint; means for determining values of the set of intensity values in accordance with the at least one linear constraint, using a constrained optimization algorithm; and means for outputting the set of intensity values, where the set of intensity values represents intensities for the set of source pixels. - View Dependent Claims (20)
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Specification