Method of optical proximity correction design for contact hole mask
Disclosed concepts include a method of optimizing an illumination profile of a pattern to be formed in a surface of a substrate. Illumination is optimized by defining a transmission cross coefficient (“TCC”) function determined in accordance with an illumination pupil and a projection pupil corresponding to an illuminator, representing at least one resolvable feature of a mask to be printed on the substrate by at least one impulse function, and creating an interference map of a predetermined order based on the at least one impulse function and the TCC function, wherein the interference map represents the at least one resolvable feature to be printed on the substrate and areas of destructive interference.
1. A method of optimizing an illumination profile of a pattern to be formed in a surface of a substrate, comprising the steps of:
defining a transmission cross coefficient (“TCC”) function determined in accordance with an illumination pupil and a projection pupil corresponding to an illuminator;
representing at least one resolvable feature comprising a contiguous area of a mask by at least one impulse function at a single point of the contiguous area; and
creating an interference map by processing the at least one impulse function with the TCC function, wherein the interference map represents the at least one resolvable feature to be printed on the substrate and areas of destructive optical interference near the resolvable feature on the substrate as a result of the mask being illuminated by the illuminator.
2. The method of optimizing an illumination profile according to claim 1 , further comprising placing an assist feature in the mask corresponding to the areas of destructive interference.
3. The method of optimizing an illumination profile according to claim 2 , wherein the assist feature is non-resolvable.
4. The method of optimizing an illumination profile according to claim 1 , wherein the interference map models light intensity incident on the substrate.
5. The method of optimizing an illumination profile according to claim 4 , further comprising placing at least one assist feature on an area of the mask corresponding to an area on the interference map having a light intensity of a predetermined level corresponding to the areas of destructive interference.
6. The method of optimizing an illumination profile according to claim 5 , wherein the predetermined level corresponds to a resolvable light intensity.
7. The method of optimizing an illumination profile according to claim 1 , wherein the interference map represents change in light intensity incident on the substrate.
8. The method of optimizing an illumination profile according to claim 1 , wherein the step of identifying the TCC function includes simplifying a complex TCC function into a simplified function having a selected number of one or more eigenvalues selected.
9. The method of optimizing an illumination profile according to claim 1 , wherein the step of creating the interference map includes convolving the at least impulse function using the identified TCC function.
10. A program product, comprising executable code transportable by at least one machine readable medium, wherein execution of the code by at least one programmable computer causes the at least one programmable computer to perform a sequence of steps for optimizing an illumination profile of a pattern to be formed in a surface of a substrate, comprising:
defining a transmission cross coefficient (“TCC”) function determined in accordance with an illumination pupil and a projection pupil corresponding to an illuminator;
representing at least one resolvable feature comprising a contiguous area of a mask by at least one impulse function at a single point of the contiguous area; and
generating an interference map by processing the at least one impulse function with the TCC function, wherein the interference map represents the at least one resolvable feature to be printed on the substrate and areas of destructive optical interference near the resolvable feature on the substrate as a result of the mask being illuminated by the illuminator.
11. The program product according to claim 10 , further comprising defining assist feature placement in the mask corresponding to the areas of destructive interference represented by the interference map.
12. The program product according to claim 10 , wherein the step of identifying the TCC function includes simplifying a complex TCC function into a simplified function having a selected number one or more eigenvalues, and wherein the created interference map has an order depending on a number of eigenvalues selected.
13. The program product according to claim 10 , wherein the step of creating the interference map includes convolving the at least impulse function using the identified TCC function.