Method of displaying model and designing pattern, and storage medium
According to one embodiment, a method of displaying model includes: sampling a pattern to acquire an attention point; calculating a spatial or planar distribution that indicates any one of a design density, a lithography target density, a mask transmittance, or an optical image intensity at N points (N being an integer equal to or greater than 1) on the pattern including the attention point; calculating a threshold for the pattern; estimating, based on the distribution and the threshold, N elements respectively corresponding to the N points as a model; and displaying the estimated model.
1. A method of displaying a model, the method comprising:
sampling a pattern of a resist to acquire M attention points, where M is an integer equal to or greater than 1;
calculating, for each of the M attention points, an optical image intensity distribution indicating an optical image intensity at each of N points including the attention point and N−1 points in a vicinity of the attention point, where N is an integer equal to or greater than 1;
calculating a development threshold for the pattern based on the optical image intensity distribution calculated for each of the M attention points;
estimating a second vector x as a resist model by solving a minimization problem of a cost function F=∥b−Ax∥2 based on a matrix A and a first vector b; and
displaying the resist model,
wherein:
the matrix A is an optical image intensity distribution matrix of M rows and N columns based on the optical image intensity distribution calculated for each of the M attention points,
the first vector b is a resist image vector having M elements and based on the calculated development threshold,
the second vector x is an integral kernel vector having N elements and configured to convert the optical image intensity distribution into the resist image vector, and
the resist model is a chemical reaction model of the resist subjected to optical imaging with the optical image intensity.
2. The method of claim 1 , wherein the attention points are acquired by sampling a border of the pattern.
3. The method of claim 2 , wherein:
the pattern comprises a resist pattern corresponding to a mask pattern,
the attention points are acquired by sampling the resist pattern, and
the optical image intensity distribution is calculated based on the mask pattern.
4. The method of claim 1 , wherein the displaying includes visualizing the model by mapping the N elements on a certain area.
5. A method of designing a pattern, the method comprising:
sampling a first pattern of a resist to acquire M attention points, where M is an integer equal to or greater than 1;
calculating, for each of the M attention points, an optical image intensity distribution indicating an optical image intensity at each of N points including the attention point and N−1 points in a vicinity of the attention point, where N is an integer equal to or greater than 1;
calculating a development threshold for the first pattern based on the optical image intensity distribution calculated for each of the M attention points;
estimating a second vector x as a resist model by solving a minimization problem of a cost function F=∥b−Ax∥2 based on a matrix A and a first vector b;
displaying the resist model; and
designing a second pattern including a design parameter of the first pattern by applying the resist model,
wherein:
the matrix A is an optical image intensity distribution matrix of M rows and N columns based on the optical image intensity distribution calculated for each of the M attention points,
the first vector b is a resist image vector having M elements and based on the calculated development threshold,
the second vector x is an integral kernel vector having N elements and configured to convert the optical image intensity distribution into the resist image vector, and
the resist model is a chemical reaction model of the resist subjected to optical imaging with the optical image intensity.
6. A non-transitory computer-readable storage medium storing a program which causes a computer to:
sample a pattern of a resist to acquire M attention points, where M is an integer equal to or greater than 1;
calculate, for each of the M attention points, an optical image intensity distribution indicating an optical image intensity at each of N points including the attention point and N−1 points in a vicinity of the attention point, where N is an integer equal to or greater than 1;
calculate a development threshold for the pattern based on the optical image intensity distribution calculated for each of the M attention points;
estimate a second vector x as a resist model by solving a minimization problem of a cost function F=∥b−Ax∥2 based on a matrix A and a first vector b; and
display the resist model,
wherein:
the matrix A is an optical image intensity distribution matrix of M rows and N columns based on the optical image intensity distribution calculated for each of the M attention points,
the first vector b is a resist image vector having M elements and based on the calculated development threshold,
the second vector x is an integral kernel vector having N elements and configured to convert the optical image intensity distribution into the resist image vector, and
the resist model is a chemical reaction model of the resist subjected to optical imaging with the optical image intensity.