Integrated mask-aware lithography modeling to support off-axis illumination and multi-tone masks

1. A computer-implemented method of performing optical lithography simulation for a multi-tone mask with a plurality of mask tones, the method comprising:

generating, using a computing device, a transmission function matrix based on a setting of the multi-tone mask; and

generating one or more convolution kernels for the multi-tone mask based on the transmission matrix, for use in transforming a formula for calculating light intensity from Abbe's form to Hopkins' form for the optical lithography simulation;

generating a set of Eigen-kernels for each mask tone based on the generated convolution kernels; and

retaining a first set of Eigen-kernels associated with a first mask tone and a second set of Eigen-kernels associated with a second mask tone,

reducing the first set and the second set of Eigen-kernels so that the first set of Eigen-kernels is larger than the second set of Eigen-kernels; and

generating model data from the reduced convolution kernels.

2. The method of claim 1 further comprising generating an analytical form for each mask tone transmission.

3. The method of claim 1 , wherein the first set of Eigen-kernels is used for major calculation and the second set of Eigen-kernels is used for accuracy enhancement.

4. The method of claim 1 further comprising saving the reduced first set and second set of Eigen-kernels into a model data.

5. The method of claim 1 , wherein the generating of the transmission function matrix comprises transforming mask transmission under each light source point to a linear combination of a plurality of Zernike functions.

6. A data processing system for performing optical lithography simulation for a multi-tone mask with a plurality of mask tones, the data processing system comprising:

a matrix generator to generate a characteristic transmission (CT) function matrix based on a setting of the multi-tone mask; and

a kernel generator to generate a set of one or more convolution kernels based on the CT function matrix, wherein the one or more convolution kernels include information for the light source and the one or more convolution kernels are used to transform a formula to calculate light intensity to Hopkins form for the optical lithography simulation;

an Eigen-kernel generator to reduce the set of one or more convolution kernels, wherein the Eigen-kernel generator reduces the set of convolution kernels by:

generating a set of Eigen-kernels for each mask tone based on the set of convolution kernels; and

retaining a first set of Eigen-kernels associated with a first mask tone and a second set of Eigen-kernels associated with a second mask tone;

and wherein the Eigen-kernel generator further reduces the set of convolution kernels by reducing the first and second sets of Eigen-kernels so that the first set of Eigen-kernels is larger than the second set of Eigen-kernels.

7. The data processing system of claim 6 , wherein the matrix generator generates the CT function matrix by transforming mask transmission under each light source point to a linear combination of a plurality of Zernike functions.

8. The data processing system of claim 6 , wherein the first set of Eigen-kernels is used for major calculation and the second set of Eigen-kernels is used for accuracy enhancement.

9. The data processing system of claim 6 , wherein the Eigen-kernel generator further records the reduced first set and second set of Eigen-kernels into a model data.

10. A computer program product stored as program code on a non-transitory computer-readable medium, the program code executable by at least one processor for performing optical lithography simulation for a multi-tone mask with a plurality of mask tones, the computer program product comprising a computer readable program code comprising instructions for:

receiving a model data that comprises a first set of Eigen-kernels associated with a first mask tone and a second set of Eigen-kernels associated with a second mask tone, the Eigen-kernels generated based on reduced convolution kernels; and

retaining the first set of Eigen-kernels associated with the first mask tone and the second set of Eigen-kernels associated with the second mask tone;

reducing the first set and the second set of Eigen-kernels so that the first set of Eigen-kernels is larger than the second set of Eigen-kernels; and computing the light intensity based on the reduced set of Eigen-kernels.

11. The computer program product of claim 10 , wherein the instructions for computing of the light intensity comprises instructions for:

generating a first Eigen-mask and a second Eigen-mask based on the model data;

generating a first partial E-field and a second partial E-field based on the first and second Eigen-masks and the first and second sets of Eigen-kernels; and

generating the light intensity by combining the first partial E-field and the second partial E-field.

12. The computer program product of claim 11 , wherein the instructions for generating of the first partial E-field and the second partial E-field comprises instructions for:

generating the first partial E-field by convolving the first Eigen-mask and the first set of Eigen-kernels; and

generating the second partial E-field by convolving the second Eigen-mask and the second set of Eigen-kernels.

13. The computer program product of claim 10 , wherein the first and second sets of Eigen-kernels are generated based on a transmission function matrix.

14. The computer program product of claim 13 , wherein the transmission function matrix is generated based on a mask topography.