Method of correcting photomask patterns
A method of predicting photoresist patterns defined by a plurality of photomask patterns is described. The measurement data of photoresist patterns defined by patterns on a photomask that are arranged similar to the photomask patterns are provided. A physical optical kernel and a mathematical load kernel as a part of a Gaussian distribution function or other distribution function or as a combined function including a part of a Gaussian distribution function or other distribution function are provided. The optimal values of the parameters of the mathematical load kernel are determined by fitting the experiment data with a simulation based on the graphic data of the patterns on the photomask and the kernels. Photoresist patterns defined by the photomask patterns are simulated based on the graphic data of the photomask patterns, the physical optical kernel, and the mathematical load kernel with the optimal values of the parameters determined.
1. A method of correcting photomask patterns, comprising:
providing measurement data of a plurality of photoresist patterns defined by patterns on a photomask that are arranged similar to the photomask patterns;
providing a physical optical kernel and a mathematical load kernel, wherein the mathematical load kernel is a part of a first Gaussian distribution function or is a combined function including a part of a first Gaussian distribution function and an entire curve of a second Gaussian distribution function different from the first Gaussian distribution function;
determining optimal values of parameters of the mathematical load kernel by fitting the measurement data with a simulation of the photoresist patterns, wherein the simulation uses graphic data of the patterns on the photomask, the physical optical kernel, and the mathematical load kernel;
simulating photoresist patterns defined by the photomask patterns using graphic data of the photomask patterns, the physical optical kernel, and the mathematical load kernel with the optimal values of the parameters determined; and
performing optical proximity correction (OPC) to modify the photomask patterns according to the simulated photoresist patterns.
2. The method of claim 1 , wherein the mathematical load kernel is a symmetric central part of the first Gaussian distribution function, and the symmetric central part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function.
3. The method of claim 1 , wherein the mathematical load kernel is a symmetric side part of the first Gaussian distribution function, and the symmetric side part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function.
4. The method of claim 1 , wherein the mathematical load kernel is a combined function including a symmetric central part of the first Gaussian distribution function, and the entire curve of the second Gaussian distribution function, and the symmetric central part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function.
5. The method of claim 1 , wherein the mathematical load kernel is a combined function including a symmetric side part of the first Gaussian distribution function, and the entire curve of the second Gaussian distribution function, and the symmetric side part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function.
6. The method of claim 1 , wherein the mathematical load kernel is a combined function including a symmetric side part of the first Gaussian distribution function, the entire curve of the second Gaussian distribution function, and a symmetric central part of a third Gaussian distribution function, the symmetric side part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function, and the symmetric central part of the third Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the third Gaussian distribution function.
7. A method of correcting photomask patterns, comprising:
simulating photoresist patterns defined by the photomask patterns using graphic data of the photomask patterns, a physical optical kernel, and a mathematical load kernel, wherein the mathematical load kernel is a part of a first Gaussian distribution function or is a combined function including a part of a first Gaussian distribution function and an entire curve of a second Gaussian distribution function different from the first Gaussian distribution function; and
performing optical proximity correction (OPC) to modify the photomask patterns according to the simulated photoresist patterns.
8. The method of claim 7 , wherein the mathematical load kernel is a symmetric central part of the first Gaussian distribution function, and the symmetric central part of the first Gaussian distribution function is symmetric with respect to an entire central axis of an entire curve of the first Gaussian distribution function.
9. The method of claim 7 , wherein the mathematical load kernel is a symmetric side part of the first Gaussian distribution function, and the symmetric side part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function.
10. The method of claim 7 , wherein the mathematical load kernel is a combined function including a symmetric central part of the first Gaussian distribution function, and the entire curve of the second Gaussian distribution function, and the symmetric central part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function.
11. The method of claim 7 , wherein the mathematical load kernel is a combined function including a symmetric side part of the first Gaussian distribution function, and the entire curve of the second Gaussian distribution function, and the symmetric side part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function.
12. The method of claim 7 , wherein the mathematical load kernel is a combined function including a symmetric side part of the first Gaussian distribution function, the entire curve of the second Gaussian distribution function, and a symmetric central part of a third Gaussian distribution function, the symmetric side part of the first Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the first Gaussian distribution function, and the symmetric central part of the third Gaussian distribution function is symmetric with respect to a central axis of an entire curve of the third Gaussian distribution function.