Method of forming a photomask layout using optical proximity correction to compensate for a three-dimensional mask effect

A method of correcting a photomask layout to compensate for a three-dimensional (3D) mask effect, the method comprising:

• receiving by a computer a layout of a mask pattern;
• obtaining one or more image parameters of a two-dimensional (2D) mask for the layout from a computer simulation;
• obtaining one or more image parameters of a 3D mask for the layout from a computer simulation;
• obtaining differences between the one or more image parameters of the 2D and 3D masks;
• compensating for the differences between the one or more image parameters of the 2D and 3D masks by
• convolving a probability function with respect to an open area, represented by a visible kernel function, Ψop, with a mask function M(x,y), to produce a first function,
• convolving a probability function with respect to a blocked area, represented by a visible kernel function, Ψbl, with the mask function M(x,y) to produce a second function, and
• summing the first function and the second function to produce a compensated vector {right arrow over (Comp)}, as expressed by
• {right arrow over (Comp)}=Cop·Ψop(x,y)M(x,y)+Cbl·Ψbl(x,y)M(x,y)+C0,
• wherein Cop, Cbl, and C0 are constants determined to minimize an error between the compensated vector {right arrow over (Comp)} and differences {right arrow over (diff)} between the image parameters of the 2D and the image parameters of the 3D masks;
• and
• correcting the photomask layout by modeling optical proximity correction (OPC) with the compensated vector {right arrow over (Comp)}.