Method and apparatus for using aerial image sensitivity to model mask errors
One embodiment of the present invention provides techniques and systems for modeling mask errors based on aerial image sensitivity. During operation, the system can receive an uncalibrated process model which includes a mask error modeling term which is based at least on an aerial image sensitivity to mask modifications which represent mask errors. Next, the system can fit the uncalibrated process model using measured CD data. Note that the mask error modeling term can also be dependent on the local pattern density. In some embodiments, the mask error modeling term can include an edge bias term and a corner rounding term. The edge bias term can be based on the sensitivity of the aerial image intensity to an edge bias, and the corner rounding term can be based on the sensitivity of the aerial image intensity to a corner rounding adjustment.
1. A computer-executed method for determining a process model, the method comprising:
receiving measured critical dimension (CD) data which was obtained by measuring CDs of features that were printed using a mask layout;
receiving an uncalibrated process model which includes a mask error modeling term which is based at least on an aerial image sensitivity to mask modifications which represent mask errors; and
determining the process model by fitting the uncalibrated process model using the measured CD data and the mask layout so that CDs predicted by the process model substantially match the measured CDs.
2. The computer-executed method of claim 1 , wherein determining the process model by fitting the uncalibrated process model using the measured CD data and the mask layout includes using a statistical fitting technique to fit an edge bias coefficient and a corner rounding coefficient.
3. The computer-executed method of claim 1 , wherein the mask error modeling term includes one or more of:
an edge bias term whose value at an evaluation point in the mask layout is based at least on an edge bias coefficient and a sensitivity of the aerial image intensity at the evaluation point to an edge bias; and
a corner rounding term whose value at the evaluation point is based at least on a corner rounding coefficient and a sensitivity of the aerial image intensity at the evaluation point to a corner rounding adjustment.
4. The computer-executed method of claim 3 , wherein the edge bias coefficient is based at least on a local pattern density at the evaluation point.
5. The computer-executed method of claim 3 , wherein the corner rounding coefficient is based at least on a local pattern density at the evaluation point.
6. A non-transitory computer-readable storage medium storing instructions that upon execution by a computer cause the computer to perform operations for determining a process model, the operations comprising:
receiving measured critical dimension (CD) data which was obtained by measuring CDs of features that were printed using a mask layout;
receiving an uncalibrated process model which includes a mask error modeling term which is based at least on an aerial image sensitivity to mask modifications which represent mask errors; and
determining the process model by fitting the uncalibrated process model using the measured CD data and the mask layout so that CDs predicted by the process model substantially match the measured CDs.
7. The computer-readable storage medium of claim 6 , wherein determining the process model by fitting the uncalibrated process model using the measured CD data and the mask layout includes using a statistical fitting technique to fit an edge bias coefficient and a corner rounding coefficient.
8. The computer-readable storage medium of claim 6 , wherein the mask error modeling term includes one or more of:
an edge bias term whose value at an evaluation point in the mask layout is based at least on an edge bias coefficient and a sensitivity of the aerial image intensity at the evaluation point to an edge bias; and
a corner rounding term whose value at the evaluation point is based at least on a corner rounding coefficient and a sensitivity of the aerial image intensity at the evaluation point to a corner rounding adjustment.
9. The computer-readable storage medium of claim 8 , wherein the edge bias coefficient is based at least on a local pattern density at the evaluation point.
10. The computer-readable storage medium of claim 8 , wherein the corner rounding coefficient is based at least on a local pattern density at the evaluation point.
11. A computer-executed method for determining an aerial image intensity value at an evaluation point, the method comprising:
determining an ideal aerial image intensity value at the evaluation point using a mask layout and an aerial image intensity model;
determining a mask error deviation value at the evaluation point using the mask layout, a modified mask layout that models mask errors, and the aerial image intensity model; and
determining the aerial image intensity value at the evaluation point by combining the ideal aerial image intensity value and the mask error deviation value.
12. The computer-executed method of claim 11 , wherein determining the mask error deviation value at the evaluation point includes computing a product of an edge bias coefficient and an edge bias sensitivity value of the aerial image intensity at the evaluation point.
13. The computer-executed method of claim 12 , wherein the edge bias coefficient is a function of a local pattern density value at the evaluation point.
14. The computer-executed method of claim 11 , wherein determining the mask error deviation value at the evaluation point includes computing a product of a corner rounding coefficient and a corner rounding sensitivity value of the aerial image intensity at the evaluation point.
15. The computer-executed method of claim 14 , wherein the corner rounding coefficient is a function of a local pattern density value at the evaluation point.
16. A non-transitory computer-readable storage medium storing instructions that upon execution by a computer cause the computer to perform operations for determining an aerial image intensity value at an evaluation point, the operations comprising:
determining an ideal aerial image intensity value at the evaluation point using a mask layout and an aerial image intensity model;
determining a mask error deviation value at the evaluation point using the mask layout, a modified mask layout that models mask errors, and the aerial image intensity model; and
determining the aerial image intensity value at the evaluation point by combining the ideal aerial image intensity value and the mask error deviation value.
17. The computer-readable storage medium of claim 16 , wherein determining the mask error deviation value at the evaluation point includes computing a product of an edge bias coefficient and an edge bias sensitivity value of the aerial image intensity at the evaluation point.
18. The computer-readable storage medium of claim 17 , wherein the edge bias coefficient is a function of a local pattern density value at the evaluation point.
19. The computer-readable storage medium of claim 16 , wherein determining the mask error deviation value at the evaluation point includes computing a product of a corner rounding coefficient and a corner rounding sensitivity value of the aerial image intensity at the evaluation point.
20. The computer-readable storage medium of claim 19 , wherein the corner rounding coefficient is a function of a local pattern density value at the evaluation point.