Local multivariable solver for optical proximity correction in lithographic processing method, and device manufactured thereby

• US 8,239,786 B2
• Filed: 12/22/2009
• Issued: 08/07/2012
• Est. Priority Date: 12/30/2008
• Status: Expired due to Fees

• Current Assignee: ASML Netherlands BV (ASML Holding NV)
• Original Assignee: ASML Netherlands BV (ASML Holding NV)
• Inventors: Wong, William S., Liu, Fei, Chen, Been-Der, Lu, Yen-Wen
• Primary Examiner(s): Doan, Nghia
• Assistant Examiner(s): Ngo, Brian
• Application Number:
  US12/644,790
• Publication Number:
  US 20100167184A1
• Time in Patent Office: 959 Days
• Field of Search: 716/50, 716/51, 716/52, 716/53, 716/54, 716/55
• US Class Current: 716/51
• CPC Class Codes: G03F 1/36 Masks having proximity correction features; Preparation thereof, e.g. optical proximity correction [OPC] design processes

Abstract

A multivariable solver for proximity correction uses a Jacobian matrix to approximate effects of perturbations of segment locations in successive iterations of a design loop. The problem is formulated as a constrained minimization problem with box, linear equality, and linear inequality constraints. To improve computational efficiency, non-local interactions are ignored, which results in a sparse Jacobian matrix.

Claims

1. A computer-implemented method comprising:

simulating a photolithography process using a design layout to produce a first simulated resist image;

perturbing each edge segment in the design layout by a selected amount to produce an initial perturbed layout;

simulating the photolithography process using the initial perturbed layout to produce a second simulated resist image;

determining a difference resist image value between the first simulated resist image and the second simulated resist image for each edge segment;

creating an n×

n matrix J such that Δ

RI=JΔ

C, where Δ

RI is an n×

1 vector of changes in resist image values and Δ

C is an n×

1 vector of changes in segment locations;

initializing the matrix J using the difference in resist image values divided by the perturbed amount;

determining a correction delta vector Δ

C by minimizing |JΔ

C+RI|²+α

|Δ

C|² subject to constraints imposed on Δ

C, wherein the correction delta vector includes a correction delta value for each edge segment and α

is a non-negative scalar;

perturbing each edge segment in the perturbed layout by the corresponding correction delta value in the correction delta vector Δ

C to create a further perturbed layout;

simulating the photolithography process using the further perturbed layout to produce a third simulated resist image;

using information from the third simulated resist image and the matrix J to produce an updated matrix J; and

updating the correction delta vector Δ

C by minimizing |JΔ

C+RI|²+α

|Δ

C|² subject to constraints imposed on Δ

C, where the updated matrix J is used in the minimization, wherein terms of the updated matrix J represent interactions between neighboring edge segments, and

wherein at least some of the steps of the method are performed using a computer.

2. The method as in claim 1, further comprising:

for each of a plurality of iterations;

perturbing each edge segment in the perturbed layout by the corresponding correction delta value in the correction delta vector Δ

C^k to create a further perturbed layout at iteration k;

simulating the photolithography process using the further perturbed layout to produce a new simulated resist image RI^k;

using information from a most recently simulated resist image RI^k and the matrix J<sup>k−

1</sup> to produce an updated matrix J^k; and

updating the correction delta vector Δ

C^k+1 by minimizing |J^kΔ

C^k+1+RI^k|²+α

|Δ

C^k+1|² subject to constraints imposed on Δ

C^k+1.

3. The method as in claim 1, wherein Δ

C is constrained by a box constraint Δ

C_min≦

Δ

C≦

Δ

C_max where Δ

C_min and Δ

C_max are n×

1 vectors specifying minimum and maximum allowable values of Δ

C.

4. The method as in claim 3, wherein Δ

C is further constrained by a linear equality constraint AΔ

C=b , where Δ

C is a correction delta vector, A is an r×

n matrix, and b is an r×

1 vector specifying r equality constraints.

5. The method as in claim 4, wherein Δ

C is further constrained by a linear inequality constraint d≦

EΔ

C≦

f, where d and f are t×

1 vectors and E is a t×

n matrix specifying t linear inequalities.

6. The method as in claim 5, wherein a total number of unknowns in the minimization is reduced by eliminating variables using the equality constraints.

7. The method as in claim 1, wherein the matrix J is updated using Broyden'"'"'s method.

8. The method as in claim 1, wherein the matrix J is updated using a Kalman filter.

9. The method as in claim 1, where the matrix J is a sparse matrix.

10. The method as in claim 2, where the matrix J is a sparse matrix.

11. The method as in claim 3, where the matrix J is a sparse matrix.

12. The method as in claim 4, where the matrix J is a sparse matrix.

13. The method as in claim 5, where the matrix J is a sparse matrix.

14. The method as in claim 6, where the matrix J is a sparse matrix.

15. The method as in claim 7, where the matrix J is a sparse matrix.

16. The method as in claim 8, where the matrix J is a sparse matrix.

17. The method as in claim 13, where a sparcity of the sparse matrix J is varied as a function of the iteration number.

18. The method as in claim 2, wherein the plurality of iterations comprises a selected number of iterations.

19. The method as in claim 2, wherein the plurality of iterations comprises continuing iterations until the simulated resist image achieves a selected figure of merit.

20. A non-transitory machine readable medium encoded with machine executable instructions for performing a method comprising:

simulating a photolithography process using a design layout to produce a first simulated resist image;

perturbing each edge segment in the design layout by a selected amount to produce an initial perturbed layout;

simulating the photolithography process using the initial perturbed layout to produce a second simulated resist image;

determining a difference resist image value between the first simulated resist image and the second simulated resist image for each edge segment;

creating an n×

n matrix J such that Δ

RI=JΔ

C, where Δ

RI is an n×

1 vector of changes in resist image values and Δ

C is an n×

1 vector of changes in segment locations;

initializing the matrix J using the difference in resist image values divided by the perturbed amount;

determining a correction delta vector Δ

C by minimizing |JΔ

C+RI|²+α

|Δ

C|² subject to constraints imposed on Δ

C, wherein the correction delta vector includes a correction delta value for each edge segment and α

is a non-negative scalar;

perturbing each edge segment in the perturbed layout by the corresponding correction delta value in the correction delta vector Δ

C to create a further perturbed layout;

simulating the photolithography process using the further perturbed layout to produce a third simulated resist image;

using information from the third simulated resist image and the matrix J to produce an updated matrix J, wherein terms of the updated matrix J represent interactions between neighboring edge segments; and

updating the correction delta vector Δ

C by minimizing |JΔ

C+RI|²+α

|Δ

C|² subject to constraints imposed on Δ

C, where the updated matrix J is used in the minimization,

wherein at least some of the steps of the method are performed using a computer.