This article was originally published online on 22 August 2011 with errors in the text. The following corrections were made on 15 September 2011 to all versions of the article:
In Eq. (6), the missing “λ” was inserted so the equation reads
$I\left( {x,y} \right) \!=\! \displaystyle\sum\limits_{n = 1}^N {{\rm \lambda }_n \left| {F^{ - 1} \left\{ {F\left\{ {K_n \left( {x,y} \right)} \right\}F\left\{ {M\left( {x,y} \right)} \right\}} \right\}} \right|} ^2$
$Ix,y=\u2211n=1N\lambda nF\u22121FKnx,yFMx,y2$,On page 3, column 1, paragraph 2, line 9, the sentence “The imaging system used for the simulations had an annular illumination source with an NA of 1.2, a wavelength (λ) of 193 nm, an outer coherence factor (σ_{out}) of 0.96, and an inner coherence factor (σ_{in}) of 0.71.” was changed to “The imaging system used for the simulations had an NA of 1.2 and an annular illumination source with a wavelength (λ) of 193 nm, an outer coherence factor (σ_{out}) of 0.96, and an inner coherence factor (σ_{in}) of 0.71.”
On page 3, column 1, paragraph 2, line 16, the phrase “where the two orthogonal polarizations, i.e., transverse electric (TE) and transverse magnetic (TM), were considered” was changed to “where the two different polarizations, i.e., transverse electric (TE) and transverse magnetic (TM) polarizations, were considered.”
On page 3, column 2, paragraph 1, line 15, the sentence “The parameters of complex transmission bands can be extracted in real time and then be applied directly to the full-chip OPC process to generate the effective mask transmission functions for two orthogonal polarizations.” was changed to “The parameters of complex transmission bands can be extracted in real time and can then be applied directly to the full-chip OPC process to generate the effective mask transmission functions for the two polarizations.”
On page 3, column 2, beneath Eq. (8), the phrase “where
$K_n^x \left( {x,y} \right)$
$Knxx,y$ and $K_n^y \left( {x,y} \right)$
$Knyx,y$ are the optical kernels for two orthogonal polarizations, M_{x}(x, y) and M_{y}(x, y) are the effective mask transmission functions for two orthogonal polarizations.” was changed to “where, for the respective polarizations, $K_n^x \left( {x,y} \right)$
$Knxx,y$ and $K_n^y \left( {x,y} \right)$
$Knyx,y$ are the optical kernels and M_{x}(x, y) and M_{y}(x, y) are the effective mask transmission functions.”On page 4, column 1, paragraph 2, line 6, the sentence “The two OPC process models, one without 3-D mask effects has 12 optical kernels, i.e., N = 12 in Eq. (5) and Eq. (6), and another with 3-D mask effects has a total of 24 optical kernels, i.e., N = 12 for two orthogonal polarizations in Eq. (7) and Eq. (8), were applied to a commercial OPC software tool.^{34}” was changed to “The two OPC process models, one without 3-D mask effects retained 12 optical kernels, i.e., N = 12 in Eq. (5) and Eq. (6), and another with 3-D mask effects retained a total of 24 optical kernels for the two polarizations, i.e., N = 12 in Eq. (7) and Eq. (8), were applied to a commercial OPC software tool.^{34}”
On page 6, column 2, following Eq. (10), the phrase “where ΔM_{x}(x, y) and ΔM_{y}(x, y) are the effective transmission functions of mask perturbations for two orthogonal polarizations” was changed to “where ΔM_{x}(x, y) and ΔM_{y}(x, y) are the effective transmission functions of mask perturbations for the respective polarizations.”
In the caption for Fig. 8, “K_{p}” was changed to “K_{p}.”
On page 7, column 2, paragraph 1, line 10, the sentence “The controller using the classical control techniques can be a proportional, P-integral (PI), P-derivative, or PI-derivative (PID) controller.” was changed to “The controller using the classical control techniques can be a proportional (P), P-integral (PI), P-derivative, or PI-derivative (PID) controller.”
On page 7, column 2, paragraph 1, line 17, the sentence “This is because the IE value is more accessible than the approximate EPE value that cannot be exactly evaluated if there is no intersection of the image intensity, and the threshold corresponding to no contour being simulated.” was changed to “This is because the IE value is more accessible than the approximate EPE value. The EPE value cannot be exactly evaluated if there is no intersection of the image intensity and the threshold, corresponding to no contour being simulated.”
In Eq. (12), the italicized “ɛ” in “
$\exists j < J\, \Rightarrow\, \| {{\bm\varepsilon }_j }\|_\infty\break \le \alpha,$
$\u2203j<J\u21d2\Vert \u025bj\Vert \u221e\u2264\alpha ,$” was un-italicized to “$\exists j < J\; \Rightarrow \; \| {{\ubvarepsilon }_j } \|_\infty\break \le \alpha,$
$\u2203j<J\u21d2\Vert \u025bj\Vert \u221e\u2264\alpha ,$”On the line following Eq. (12) page 9, paragraph 3, line 6, the italicized “ɛ” in “
${\bm\varepsilon}$
$\u025b$_{j}” was un-italicized to “${\ubvarepsilon}$
$\u025b$_{j}”On page 10, column 2, line 2, the variable “K_{d}” was changed to “K_{d}.”
On page 11, column 1, paragraph 2, line 18, the sentence “This is because the run time is strongly dependent on the chip size (up to several hundred square millimeters), the number of segments, and the technology node.” was changed to “This is because the run time is strongly dependent on the chip area (e.g., typically up to several hundred square millimeters), the number of segments, and the technology node.”
On page 11, column 2, paragraph 1, line 8, the sentence “The average range for the three critical layers is reduced to ∼16%, showing that the non-DCOPC methodology does a good job.” was changed to “However, the average range for the three critical layers is reduced by ∼16%, showing that the non-DCOPC methodology does a good job.”
On page 13, column 1, end of the first paragraph, a sentence was added: “The concept of non-DCOPC can also be applied to extreme ultraviolet lithography and e-beam lithography.”
On page 14, column 1, last line, the phrase “deep ultraviolet microlithography scanners” was changed to “deep ultraviolet lithography scanners.”