Inverse Mask Design and Correction for Electronic Design

Abstract

Various implementations of the invention provide for the generation of “smooth” mask contours by inverse mask transmission derivation and by subsequently “smoothing” the derived mask contours by proximity correction.

Description

RELATED APPLICATIONS[0001]This application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application No. 61 / 154,271 entitled “Extreme Optical Process Correction,” filed on Feb. 20, 2010, and naming Yuri Granik et al. as inventors, and is a continuation in part of U.S. application Ser. No. 12 / 416,016 entitled “Calculation System for Inverse Masks,” filed Mar. 31, 2009, and naming Yuri Granik as inventor, which in turn claims the benefit of U.S. Provisional Patent Application No. 61 / 041,197, filed Mar. 31, 2008 and is itself a continuation in part of U.S. application Ser. No. 12 / 359,174, filed Jan. 23, 2009, which in turn claims the benefit of U.S. Provisional Patent Application No. 60 / 792,476 filed Apr. 14, 2006, and is a continuation in part of U.S. patent application Ser. No. 11 / 364,802 filed Feb. 28, 2006, which in turn claims the benefit of U.S. Provisional Patent Application No. 60 / 657,260 filed Feb. 28, 2005; U.S. Provisional Patent Application No. 60 / 658,2...

AI Technical Summary

Benefits of technology

"The invention allows for creating smooth mask contours by first generating them using inverse mask transmission and then smoothing them by proximity correction. This results in a smoother and more accurate mask for use in various applications."

Problems solved by technology

The direct problem of optical microlithography is to print features on a wafer under given mask, imaging system, and process characteristics.

When partially coherent optics (4) is considered, the problem is complicated by the interactions mimj* between pixels and becomes a quadratic programming (QP) problem.

Reduction to LP is possible; however, the leanest relevant to microlithography and rigorous formulation must account for the partial coherence, so that the problem is intrinsically not simpler than QP.

The drawback is that pixel flipping can easily get stuck in the local minima, especially for PSM optimizations.

This however requires substantial simplifications.

Nashold projections belong to the class of the image restoration techniques, rather than to the image optimizations, meaning that the method might not find the solution (because it does not exists at all), or in the case when it does converge, we cannot state that this solution is the best possible.

Gerchberg-Saxton iterations tend to stagnate.

The behavior of iterates (32) is not yet sufficiently understood [36], which complicates choice of α,γ.

The convergence is slow because T is large, so that application to the large layout areas is problematic.

If we remove constraints, the problem becomes unbounded, with no minimum and no solutions.

If there is at least one dark and one bright pixel, the problem is indefinite.

This has important implications for the type of the applicable numerical methods: in large problems we can use factorizations of matrix Q, in huge problems factorizations are unrealistic.

The solutions of (55) increase image fidelity; however, the numerical experiments show that the contour fidelity of the images is not adequate.

The branch-and-bound global search techniques [18] are not the right choice because they are not well-suited for the large multi-dimensional optimization problems.

This algorithm calculates the objective function numerous times; however, the runtime cost of its exploratory calls is relatively low with the electrical field caching (see the next section).

The assist features become more and more complicated as the descent iterations improve objective function.

The direct problem of microlithography is to simulate printing features on the wafer under given mask, imaging system, and process characteristics.

When partially coherent optics (4A) is considered, the problem is complicated by the interactions mimj* between pixels and becomes a quadratic programming (QP) problem.

Reduction to LP is possible; however, the leanest relevant to microlithography and rigorous formulation must account for the partial coherence, so that the problem is intrinsically not simpler than QP.

The drawback is that pixel flipping can easily get stuck in the local minima, especially for PSM optimizations.

Images