Method, program product and apparatus for improving calibration of resist models used in critical dimension calculation

1. A method for calibrating a resist model used in critical dimension (CD) calculation, comprising the steps of:

obtaining a dose function indicating the amount of energy in a resist based on optical tool to be used to form the resist on a wafer; and

convolving the dose function with a convolution kernel to obtain a modified dose function, the convolution kernel having variable diffusion lengths in different directions.

2. The method according to claim 1 , further comprising:

converting the modified dose function into a CD value;

comparing the CD value with a target value; and

adjusting the diffusion lengths of the convolution kernel based on the comparison result.

3. The method according to claim 1 , wherein the convolution kernel includes multiple Gaussian kernels each having variable diffusion lengths in different directions.

4. The method according to claim 3 , wherein the convolution kernel includes eight Gaussian kernels represented by the following equation:

WzW1 G(Lx1, Ly1, Lz1; x,y,z)+WzW2 G(Lx2, Ly1, Lz1; x,y,z)+WzW3 G(Lx1, Ly2, Lz1; x,y,z)+Wz(1−W1−W2−W3)G(Lx2, Ly2, Lz1; x,y,z)+(1−Wz)W1 G(Lx1, Ly1, Lz2; x,y,z)+(1−Wz)W2 G(Lx2, Ly1, Lz2; x,y,z)+(1−Wz)W3 G(Lx1, Ly2, Lz2; x,y,z)+(1−Wz)(1−W1−W2−W3)G(Lx2, Ly2, Lz2; x,y,z),

where Lx 1 , Ly 1 and Lz 1 are a first set of diffusion lengths in x, y and z directions, respectively, and Lx 2 , Ly 2 and Lz 2 are a second set of diffusion lengths in x, y and z directions, respectively, and

W 1 , W 2 , W 3 and Wz are weights.

5. The method according to claim 4 , wherein

weights W 1 , W 2 , W 3 and Wz are non-negative,

weights W 1 , W 2 and W 3 are bounded by 1, and

weight Wz is bounded by 1.

6. A computer program product having a computer readable medium bearing a computer program for calibrating a resist model used in critical dimension (CD) calculation, the computer program, when executed, causing a computer to perform the steps of:

obtaining a dose function indicating the amount of energy in a resist based on optical tool to be used to form the resist on a wafer; and

convolving the dose function with a convolution kernel to obtain a modified dose function, the convolution kernel having variable diffusion lengths in different directions.

7. The computer program product according to claim 6 , further comprising the steps of:

converting the modified dose function into a CD value;

comparing the CD value with a target value; and

adjusting the diffusion lengths of the convolution kernel based on the comparison result.

8. The computer program product according to claim 6 , wherein the convolution kernel includes multiple Gaussian kernels each having variable diffusion lengths in different directions.

9. The computer program product according to claim 8 , wherein the convolution kernel includes eight Gaussian kernels represented by the following equation:

WzW1 G(Lx1, Ly1, Lz1; x,y,z)+WzW2 G(Lx2, Ly1, Lz1; x,y,z)+WzW3 G(Lx1, Ly2, Lz1; x,y,z)+Wz(1−W1−W2−W3)G(Lx2, Ly2, Lz1; x,y,z)+(1−Wz)W1 G(Lx1, Ly1, Lz2; x,y,z)+(1−Wz)W2 G(Lx2, Ly1, Lz2; x,y,z)+(1−Wz)W3 G(Lx1, Ly2, Lz2; x,y,z)+(1−Wz)(1−W1−W2−W3)G(Lx2, Ly2, Lz2; x,y,z),

where Lx 1 , Ly 1 and Lz 1 are a first set of diffusion lengths in x, y and z directions, respectively, and Lx 2 , Ly 2 and Lz 2 are a second set of diffusion lengths in x, y and z directions, respectively, and

W 1 , W 2 , W 3 and Wz are weights.

10. The computer program according to claim 9 , wherein

weights W 1 , W 2 , W 3 and Wz are non-negative,

weights W 1 , W 2 and W 3 are bounded by 1, and

weight Wz is bounded by 1.

11. An apparatus for calibrating a resist model used in critical dimension (CD) calculation, comprising:

a first unit configured for obtaining a dose function indicating the amount of energy in a resist based on optical tool to be used to form the resist on a wafer; and

a second unit configured for convolving the dose function with a convolution kernel to obtain a modified dose function, the convolution kernel having variable diffusion lengths in different directions.

12. The apparatus according to claim 11 , further comprising:

a third unit configured for converting the modified dose function into a CD value;

a fourth unit configured for comparing the CD value with a target value; and

a fifth unit configured for adjusting the diffusion lengths of the convolution kernel based on the comparison result.

13. The apparatus according to claim 11 , wherein the convolution kernel includes multiple Gaussian kernels each having variable diffusion lengths in different directions.

14. The apparatus according to claim 13 , wherein the convolution kernel includes eight Gaussian kernels represented by the following equation:

WzW1 G(Lx1, Ly1, Lz1; x,y,z)+WzW2 G(Lx2, Ly1, Lz1; x,y,z)+WzW3 G(Lx1, Ly2, Lz1; x,y,z)+Wz(1−W1−W2−W3)G(Lx2, Ly2, Lz1; x,y,z)+(1−Wz)W1 G(Lx1, Ly1, Lz2; x,y,z)+(1−Wz)W2 G(Lx2, Ly1, Lz2; x,y,z)+(1−Wz)W3 G(Lx1, Ly2, Lz2; x,y,z)+(1−Wz)(1−W1−W2−W3)G(Lx2, Ly2, Lz2; x,y,z),

where Lx 1 , Ly 1 and Lz 1 are a first set of diffusion lengths in x, y and z directions, respectively, and Lx 2 , Ly 2 and Lz 2 are a second set of diffusion lengths in x, y and z directions, respectively, and

W 1 , W 2 , W 3 and Wz are weights.

15. The apparatus according to claim 14 , wherein

weights W 1 , W 2 , W 3 and Wz are non-negative,

weights W 1 , W 2 and W 3 are bounded by 1, and

weight Wz is bounded by 1.