Gradient-Based Search Mechanism for Optimizing Photolithograph Masks

A computer program product comprising a computer recordable medium having a computer readable program recorded thereon, wherein the computer readable program, when executed on a computing device, causes the computing device to:

• receive a given target pattern;
• generating an initial fictitious mask;
• select an initial value of α2, wherein the initial value of α2 is used to determine a light intensity and a wafer image;
• determine the light intensity for each pixel in the initial fictitious mask, wherein the computer readable program to determine the light intensity uses the following equation:
• I
• j
• =
• ∑
• k
• =
• 1
• m
• 
• σ
• k
• 
• 
• ∑
• i
• =
• 1
• MN
• 
• φ
• ijk
• 
• S
• 2
• 
• (
• θ
• i
• )
• 
• 2
• wherein Ij is the light intensity at pixel location j, wherein θ is a specific pixel, wherein m is an eigenvector of the kernel, wherein M is a number of grids in a x direction, wherein N is a number of grids in ay direction, wherein S2 is a logistic function, wherein a is the eigenvalue of the optical kernel function, wherein φ is eigenvector of the optical kernel function, wherein k is the kernel index, and wherein i is the grid index;
• determine the wafer image for each pixel in the initial fictitious mask;
• determine if a convergence has been achieved by comparing the wafer image generated from the initial fictitious mask to the given target pattern;
• and
• responsive to a convergence of the wafer image generated from the initial fictitious mask to the given target pattern, generate a final mask to use to transfer an image to a wafer.

An apparatus, comprising:

• a processor, and
• a memory coupled to the processor, wherein the memory comprises instructions which, when executed by the processor, cause the processor to:
• receive an initial photolithograph mask and a given target pattern;
• generate an initial fictitious mask;
• select an initial value of α2, wherein the initial value of α2 is used to determine a light intensity and a wafer image;
• determine the light intensity for each pixel in the initial fictitious mask, wherein the instructions to determine the light intensity uses the following equation:
• I
• j
• =
• ∑
• k
• =
• 1
• m
• 
• σ
• k
• 
• 
• ∑
• i
• =
• 1
• MN
• 
• φ
• ijk
• 
• S
• 2
• 
• (
• θ
• i
• )
• 
• 2
• wherein Ij is the light intensity at pixel location I, wherein θ is a specific pixel, wherein m is an eigenvector of the kernel, wherein M is a number of grids in a x direction, wherein N is a number of grids in a y direction, wherein S2 is a logistic function, wherein a is the eigenvalue of the optical kernel function;
• wherein φ is eigenvector of the optical kernel function, wherein k is the kernel index, and wherein i is the grid index;
• determine the wafer image for each pixel in the initial fictitious mask;
• determine if a convergence has been achieved by comparing the wafer image generated from the initial fictitious mask to the given target pattern;
• and
• responsive to a convergence of the wafer image generated from the initial fictitious mask to the given target pattern, generate a final mask to use to transfer an image to a wafer.