Method for making masks

A method for designing masks for optical lithography, wherein an initial mask provides an output image having a binary configuration wherein said image is zero in domain A and one in domain B and wherein contour C surrounds the boundaries of A and is in region A and wherein contour D surrounds the boundaries of B and is in region B and wherein said mask has output intensity values, I, at said A, B, C and D, the threshold values of which produce said output images within constraints such that, ##EQU25## and wherein x represents spatial location (x,y) and a, b, c and d are corresponding intensity threshold values in regions A, B, C and D respectively, and wherein said mask image is quantized into small square pixels represented by vector of pixel variables a, wherein a is an element of a mask transmission function, said method comprising the steps of:

• defining sampling points which are representative of said A, B, C and D;
• defining indices for said sampling points to be k;
• defining a set of indices of said sampling points in a region i wherein i=A, B, C or D to be N.sub.i ;
• determining whether said output intensity values of said sampling points are within said constraints;
• defining local objective functions, h.sub.i (I(x.sub.k,a)), which includes a non-linear error function, e.sub.k, represenative of said determination step, and includes a penalty factor, .lambda..sub.i, reflective of the relative importance of each of said constraints, wherein said local objective functions provide that ##EQU26## and wherein said error function e.sub.k (I(x.sub.k,a)) provides that ##EQU27## combining said local objective functions to give a total objective function, H(a), which is minimized for optimization, wherein said total objective provides that ##EQU28## adjusting said mask pattern to provide for minimization by optimization of said total objective function;
• transferring said mask pattern to a mask generating machine to generate a mask;
• and
• generating a mask.

A method for making masks for optical lithography or other projection printing, wherein said mask is represented by an initial mask pattern and wherein said mask provides a first output image on a resist developed wafer having a substantially binary configuration on a wafer, wherein on said wafer, A and B represent regions on a resist developed wafer, and wherein said output image is zero in domain A and one in domain B, and wherein as light is applied to said mask, said mask allows light to pass through it and onto a wafer at varying intensities, such intensities represented by output intensity values, I, at said and the threshold values of which produce said output images within constraints such that, ##EQU29## and wherein x represents spatial location on said wafer (x,y) and a and b are corresponding intensity threshold values at A and B respectively, and wherein the mask pattern is quantized into pixels represented by vector of pixel variables a, said method comprising the steps of:

• defining sampling points which are representative of said A and B;
• defining indices for said sampling points to be k;
• defining a set of indices of said sampling points in a region i wherein i=A or B to be N.sub.i ;
• defining local objective functions, h.sub.i (I(x.sub.k,a)), which include error functions, e.sub.k, representative of the degree to which said output intensity values of said sampling points are within said constraints, and which include a penalties, .lambda..sub.i, reflective of the relative importance of each of said regions and contours, wherein said local objective functions provide that ##EQU30## and wherein said error function e.sub.k (I(x.sub.k,a)) provides that ##EQU31## combining said local objective functions to give a total objective function, H(a), wherein said total objective provides that ##EQU32## adjusting said total objective function to provide for minimization by optimization of said total objective function;
• and
• transferring said mask pattern to a mask generating machine to generate a mask;
• and
• generating a mask.