Method of estimating shape of chemically amplified resist

A method for estimating a shape of a chemically amplified resist by a computer simulation, comprising the steps of:

• calculating diffusion of a catalyst species in the chemically amplified resist upon post-baking process by approximation with a Gaussian distribution G(x′, y′), represented as:
• G(x′, y′)=(1/(2πdl2))exp(−(x′2+y′2)/(2dl2))
• wherein dl is a diffusion length;
• calculating a light intensity distribution on the chemically amplified resist upon the exposure to light when a mask pattern of a simulation object is used wherein said light intensity distribution, I(x,y) is calculated in accordance with:
• I(x,y)=∫∫S(p, q)[∫∫F(xo, yo)K(x−xo, y−yo)exp((i2π)/λ(pxo+qyo))dxo dyo]2dpdq
• where
• x and y are two-dimensional coordinate values representative of a point on a wafer, S, which is a function representative of an effective light source, is a function representative of an intensity of light at a point (p,q) on the light source, F is a function representative of a mask transmittance at a point (xo, yo) on the mask, K is a pupil function, λ an exposure light wavelength, i an imaginary unit such that i232 −1, and π is a circular constant, said pupil function K being represented as:
• K(x,y)=Ko(x,y)exp((2πifNA2(x2+y2))/(λa2))
• where f is a focus value, NA a numerical aperture, a an aperture diameter, with Ko(x,y) being 1 if (x2+y2)/a2 is less than or equal to 1 and 0 otherwise;
• correcting the light intensity distribution with the Gaussian distribution producing a corrected light intensity J(x,y) formed by a convolution integration of light intensity distribution I(x,y) represented by:
• J(x,y)=∫∫I(x−x′, y−y′)G(x′, y′)dx′dy′;
• calculating a shape of a two-dimensional pattern of the chemically amplified resist based on the corrected light intensity distribution J(x,y) at arbitrary threshold value Ith;
• and
• repeating the calculation of the light intensity distribution, the correction of the light intensity distribution and the calculation of the shape of the two-dimensional pattern while the mask pattern is corrected until the two-dimensional pattern obtained by the calculation of the shape becomes a desired shape.

A recording medium which stores a program for estimating a shape of a chemically amplified resist by a computer simulation and is readable by a computer, said program causing said computer to execute the steps of:

• calculating diffusion of a catalyst species in the chemically amplified resist upon post-baking process by approximation with a Gaussian distribution G(x′, y′), represented as:
• G(x′, y′)=(1/(2πdl2))exp(−(x′2+y′2)/(2dl2))
• wherein dl is a diffusion length;
• calculating a light intensity distribution on the chemically amplified resist upon exposure to light wherein said light intensity distribution, I(x,y) is calculated in accordance with:
• I(x,y)=∫∫S(p, q)[∫∫F(xo, yo)K(x−xo, y−yo)exp((i2π)/λ(pxo+qyo))dxo dyo]2dpdq
• where
• x and y are two-dimensional coordinate values representative of a point on a wafer, S, which is a function representative of an effective light source, is a function representative of an intensity of light at a point (p,q) on the light source, F is a function representative of a mask transmittance at a point (xo, yo) on the mask, K is a pupil function, λ an exposure light wavelength, i an imaginary unit such that i2=−1, and π is a circular constant, said pupil function K being represented as:
• K(x,y)=Ko(x,y)exp((2πifNA2(x2+y2))/(λa2))
• where f is a focus value, NA a numerical aperture, a an aperture diameter, with Ko(x,y) being 1 if (x2+y2)/a2 is less than or equal to 1 and 0 otherwise;
• correcting the light intensity distribution with the Gaussian distribution producing a corrected light intensity J(x,y) formed by a convolution integration of light intensity distribution I(x,y) represented by:
• J(x,y)=∫∫I(x−x′, y−y′)G(x′, y′)dx′dy′;
• performing calculation of the shape of a two-dimensional pattern of the chemically amplified resist based on the corrected light intensity distribution J(x,y) at arbitrary threshold value Ith;
• and
• correcting focus displacement arising from a film thickness of the chemically amplified resist.

A recording medium which stored a program estimating a shape of a chemically amplified resist by a computer simulation and is readable by a computer, said program causing said computer to execute the steps of:

• calculating diffusion of a catalyst species in the chemically amplified resist upon a post-baking process by approximation with a Gaussian distribution G(x′, y′), represented as:
• G(x′, y′)=(1(2πdl2))exp(−(x′2+y′2)/(2dl2))
• wherein dl is a diffusion length;
• calculating a light intensity distribution on the chemically amplified resist upon the exposure of light when a mask pattern of a simulation object is used wherein said light intensity distribution, I(x,y) is calculated in accordance with:
• I(x,y)=∫∫S(p, q)[∫∫F(xo, yo)K(x−xo, y−yo)exp((i2π)/λ(pxo+qyo))dxo dyo]2dpdq
• where
• x and y are two-dimensional coordinate values representative of a point on a wafer, S, which is a function representative of an effective light source, is a function representative of an intensity of light at a point (p,q) on the light source, F is a function representative of a mask transmittance at a point (xo, yo) on the mask, K is a pupil function, λ an exposure light wavelength, i an imaginary unit such that i2=1, and π is a circular constant, said pupil function K being represented as:
• K(x,y)=Ko(x,y)exp((2πifNA2(x2+y2))/(λa2))
• where f is a focus value, NA a numerical aperture, a an aperture diameter, with Ko(x,y) being 1 if (x2+y2)/a2 is less than or equal to 1 and 0 otherwise;
• correcting the light intensity distribution with the calculated Gaussian distribution producing a corrected light intensity J(x,y) formed by a convolution integration of light intensity distribution I(x,y) represented by:
• J(x,y)=∫∫I(x−x′, y−y′)G(x′, y′)dx′dy′;
• calculating a shape of a two-dimensional pattern of the chemically amplified resist based on the corrected light intensity distribution J(x,y) at arbitrary threshold value Ith;
• and
• repeating the calculation of the light intensity distribution, the correction of the light intensity distribution and the calculation of the shape of the two-dimensional pattern while the mask patter is corrected until the two-dimensional pattern obtained by the calculation of the shape becomes a desired shape.

A computerized method of estimating a shape of a chemically amplified photoresist, comprising the steps of:

• calculating an uncorrected light intensity distribution on the chemically amplified photoresist upon exposure to light energy of at least a predetermined exposing energy wherein said light intensity distribution, I(x,y) is calculated in accordance with:
• I(x,y)=∫∫S(p, q)[∫∫F(xo, yo)K(x−xo, y−yo)exp((i2π)/λ(pxo+qyo))dxo dyo]2dpdq
• where
• x and y are two-dimensional coordinate values representative of a point on a wafer, S, which is a function representative of an effective light source, is a function representative of an intensity of light at a point (p,q) on the light source, F is a function representative of a mask transmittance at a point (xo, yo) on the mask, K is a pupil function, λ an exposure light wavelength, i an imaginary unit such that i2=−1, and π is a circular constant, said pupil function K being represented as:
• K(x,y)=Ko(x,y)exp((2πifNA2(x2+y2))/(λa2))
• where f is a focus value, NA a numerical aperture, a an aperture diameter, with Ko(x,y) being 1 if (x2+y2)/a2 is less than or equal to 1 and 0 otherwise;
• calculating a two dimensional Gaussian distribution of a catalyst species in the chemically amplified photoresist upon a post-baking process, including a least squares fit of linear line and space patterns, wherein the Gaussian distribution is described using a single value of a distribution broadening parameter;
• correcting the uncorrected light intensity distribution to calculate a corrected light intensity distribution using a convolution integration method with the distribution broadening parameter of the Gaussian distribution, G(x′y′), producing a corrected light intensity J(x,y) formed by a convolution integration of light intensity distribution I(x,y) represented by:
• J(x,y)=∫∫I(x−x′, y−y′)G(x′, y′)dx′dy′;
• and
• calculating the shape of the photoresist using the corrected light intensity distribution J(x,y) at arbitrary threshold value Ith.