Method and system for determining in-plane distortions in a substrate
The determination of in-plane distortions of a substrate includes measuring one or more out-of-plane distortions of the substrate in an unchucked state, determining an effective film stress of a film on the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state, determining in-plane distortions of the substrate in a chucked state based on the effective film stress of the film on the substrate in the unchucked state and adjusting at least one of a process tool or an overlay tool based on at least one of the measured out-of-plane distortions or the determined in-plane distortions.
1. A system for determining in-plane distortions of a substrate comprising:
a substrate geometry measurement tool configured to measure out-of-plane distortions of the substrate in an unchucked state; and
a controller communicatively coupled to the measurement tool, the controller including one or more processors configured to execute a set of program instructions, the program instructions configured to cause the one or more processors to:
receive one or more measurement results indicative of out-of-plane distortions of the substrate in the unchucked state from the measurement tool;
determine an effective surface film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state with a two-dimensional plate model;
determine in-plane distortions of the substrate in a chucked state based on the effective surface film stress of the substrate in the unchucked state with the two-dimensional plate model; and
provide the at least one of the measured out-of-plane distortions or the determined in-plane distortions to at least one of a process tool or a metrology tool to adjust the at least one of the process tool or the metrology tool based on the at least one of the measured out-of-plane distortions or the determined in-plane distortions.
2. The system of claim 1 , wherein the substrate geometry measurement tool comprises:
a dual Fizeau interferometer.
3. The system of claim 1 , wherein the determining an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state with a two-dimensional plate model comprises:
applying a fitting function to the measured out-of-plane distortions; and
determining the effective film stress of the substrate in the unchucked state based on the fitted function with the two-dimensional plate model.
4. The system of claim 3 , wherein the fitting function comprises:
a Zernike polynomial.
5. The system of claim 1 , wherein the determining an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state with a two-dimensional plate model comprises:
applying a finite difference approximation to determine the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
6. The system of claim 1 , wherein the determining an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state with a two-dimensional plate model comprises:
applying a finite element approximation to determine the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
7. The system of claim 1 , wherein the determining an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state with a two-dimensional plate model comprises:
applying a finite volume approximation to determine the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
8. The system of claim 1 , wherein the determining in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model comprises:
applying a finite difference approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
9. The system of claim 1 , wherein the determining in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model comprises:
applying a finite element approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
10. The system of claim 1 , wherein the determining in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model comprises:
applying a finite volume approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
11. The system of claim 1 , wherein the determining in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model comprises:
applying a method of moments approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
12. The system of claim 1 , wherein the metrology tool comprises:
an overlay metrology tool.
13. The system of claim 1 , wherein the substrate comprises:
a semiconductor wafer.
14. A system for determining in-plane distortions of a substrate comprising:
a substrate geometry measurement tool configured to measure out-of-plane distortions of the substrate in an unchucked state; and
a controller communicatively coupled to the measurement tool, the controller including one or more processors configured to execute a set of program instructions, the program instructions configured to cause the one or more processors to:
receive one or more measurement results indicative of out-of-plane distortions of the substrate in the unchucked state from the measurement tool;
apply a two-dimensional plate model to determine in-plane distortions of the substrate in a chucked state based on the out-of-plane distortions of the substrate in the unchucked state; and
provide the at least one of the measured out-of-plane distortions or the determined in-plane distortions to at least one of a process tool or an overlay tool to adjust the at least one of the process tool or the overlay tool based on the at least one of the measured out-of-plane distortions or the determined in-plane distortions.
15. A system for determining in-plane distortions of a substrate comprising:
a substrate geometry measurement tool configured to measure out-of-plane distortions of the substrate in an unchucked state; and
a controller communicatively coupled to the measurement tool, the controller including one or more processors configured to execute a set of program instructions, the program instructions configured to cause the one or more processors to:
receive one or more measurement results indicative of out-of-plane distortions of the substrate in the unchucked state from the measurement tool;
apply an Euler-Lagrange plate model to determine in-plane distortions of the substrate in a chucked state based on the out-of-plane distortions of the substrate in the unchucked state; and
provide the at least one of the measured out-of-plane distortions or the determined in-plane distortions to at least one of a process tool or an overlay tool to adjust the at least one of the process tool or the overlay tool based on the at least one of the measured out-of-plane distortions or the determined in-plane distortions.
16. A method for determining in-plane distortions of a substrate comprising:
measuring one or more out-of-plane distortions of the substrate in an unchucked state;
determining, with a two-dimensional plate model, an effective film stress of a film on the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state;
determining, with the two-dimensional plate model, in-plane distortions of the substrate in a chucked state based on the effective film stress of the film on the substrate in the unchucked state; and
providing the at least one of the measured out-of-plane distortions or the determined in-plane distortions to at least one of a process tool or an overlay tool to adjust the at least one of the process tool or the overlay tool based on the at least one of the measured out-of-plane distortions or the determined in-plane distortions.
17. The method of claim 16 , wherein the determining, with a two-dimensional plate model, an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state comprises:
applying a fitting function to determine the effective film stress of the substrate in the unchucked state; and
determining the effective film stress of the substrate in the unchucked state based on the fitted function with the two-dimensional plate model.
18. The method of claim 16 , wherein the determining, with a two-dimensional plate model, an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state comprises:
applying a finite difference approximation to determine the effective film stress of the substrate in the unchucked state.
19. The method of claim 16 , wherein the determining, with a two-dimensional plate model, an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state comprises:
applying a finite element approximation to determine the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
20. The method of claim 16 , wherein the determining, with a two-dimensional plate model, an effective film stress of the substrate in the unchucked state based on the measured out-of-plane distortions of the substrate in the unchucked state comprises:
applying a finite volume approximation to determine the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
21. The method of claim 16 , wherein the determining, with the two-dimensional plate model, in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state comprises:
applying a finite difference approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
22. The method of claim 16 , wherein the determining, with the two-dimensional plate model, in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state comprises:
applying a finite element approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
23. The method of claim 16 , wherein the determining, with the two-dimensional plate model, in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state comprises:
applying a finite volume approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.
24. The method of claim 16 , wherein the determining, with the two-dimensional plate model, in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state comprises:
applying a method of moments approximation to determine the in-plane distortions of the substrate in a chucked state based on the effective film stress of the substrate in the unchucked state with the two-dimensional plate model.