Patent ID: 7954073

Claim:
A computer-implemented method of arranging mask patterns, the method comprising: obtaining a distribution of functions h(ξ−x) representing the contribution of an assist feature to image intensity on a main feature, wherein x is the position of the main feature and ξ is the position of the assist feature, wherein (ξ−x) represents displacement between the main feature and the assist feature, and wherein the distribution of the functions h(ξ−x) satisfy I ⁡ ( x ) - I 0 ⁡ ( x ) 2 ⁢ I 0 ⁡ ( x ) = h ⁡ ( ξ - x ) ⁢ ⁢ m ⁡ ( ξ ) ⁢ Δ ⁢ ⁢ ξ , where I(x) is an image intensity on the main feature when the assist feature is present, I 0 (x) is an image intensity on the main feature when the assist feature is not present, and m(ξ) is a mask transmittance; discretizing neighboring regions of the main feature into finite regions and discretizing the distribution of the functions h(ξ−x) into the finite regions to generate a distribution of discretized values ĥ(x,ξ) consisting of ĥ 0 , ĥ 1 , ĥ 2 , . . . , ĥ N ; generating from the distribution of discretized values ĥ(x,ξ) a distribution of representative values h (x,ξ) consisting of h 0 , h 1 , h 2 , . . . , h N and that satisfy { h _ I ⁢ : ⁢ 0 ≤ I ≤ N } = { h ^ I ⁢ : ⁢ 0 ≤ I ≤ N } when ⁢ ⁢ I ≥ J , ⁢  h _ I  ≥  h _ J  ; determining a position of the assist feature by using polygonal regions having the same h (x,ξ); and generating, by a computer, a mask pattern using the determined position of the assist feature.