Mask bias approximation

1. A method of optimizing a mask used to produce a design pattern, the method comprising:

generating a mask image for the mask;

biasing the mask image to obtain a biased mask image by updating at least one pixel of the mask image using an interpolation of neighboring pixels of the at least one pixel, the interpolation being dependent on a predetermined value relating to a bias value; and

simulating the biased mask image to obtain a wafer image to be compared to the design pattern.

2. The method of claim 1 , wherein the interpolation is based on a Taylor expansion.

3. The method of claim 2 , wherein the Taylor expansion is a first order Taylor expansion.

4. The method of claim 2 , further comprising performing the Taylor expansion with respect to the predetermined value.

5. The method of claim 1 , wherein the neighboring pixels comprise non-integer pixel locations.

6. The method of claim 1 , wherein the neighboring pixels are defined by a size of a Hamming-sinc filter.

7. The method of claim 1 , wherein the predetermined value is a bias value corresponding to an error by an ebeam machine for use in producing the mask.

8. An apparatus for optimizing a mask used to produce a design pattern, the apparatus comprising:

a processor system; and

a memory configured to store instructions executable by the processor system, the instructions, upon execution by the processor system, configured to cause the processor system to at least:

generate a mask image for the mask;

bias the mask image to obtain a biased mask image by updating at least one pixel of the mask image using an interpolation of neighboring pixels of the at least one pixel, the interpolation being dependent on a predetermined value relating to a bias value; and

simulate the biased mask image to obtain a wafer image to be compared to the design pattern.

9. The apparatus of claim 8 . . . wherein the interpolation is based on a Taylor expansion.

10. The apparatus of claim 9 , wherein the Taylor expansion is a first order Taylor expansion.

11. The apparatus of claim 9 , wherein the instructions are further configured to cause the processor system to perform the Taylor expansion with respect to the predetermined value.

12. The apparatus of claim 8 , wherein the neighboring pixels comprise non-integer pixel locations.

13. The apparatus of claim 8 , wherein the neighboring pixels are defined by a size of a Hamming-sinc filter.

14. The apparatus of claim 8 , wherein the predetermined value is a bias value corresponding to an error by an ebeam machine for use in producing the mask.

15. A non-transitory computer-readable storage medium, comprising instructions therein, which instructions, when executed by a processor system, are configured to cause the processor system to at least:

generate a mask image for a mask to be used to produce a design pattern;

bias the mask image to obtain a biased mask image by updating at least one pixel of the mask image using an interpolation of neighboring pixels of the at least one pixel, the interpolation being dependent on a predetermined value relating to a bias value; and

simulate the biased mask image to obtain a wafer image to be compared to the design pattern.

16. The non-transitory computer-readable storage medium of claim 15 , wherein the interpolation is based on a Taylor expansion.

17. The non-transitory computer-readable storage medium of claim 16 , wherein the Taylor expansion is a first order Taylor expansion.

18. The non-transitory computer-readable storage medium of claim 15 , wherein the neighboring pixels comprise non-integer pixel locations.

19. The non-transitory computer-readable storage medium of claim 15 , wherein the neighboring pixels are defined by a size of a Hamming-sinc filter.

20. The non-transitory computer-readable storage medium of claim 15 , wherein the predetermined value is a bias value corresponding to an error by an ebeam machine for use in producing the mask.