CN100338611C - Modeling method for integrated circuit photolithography manufacturing based on convolution kernel - Google Patents

Abstract

The present invention discloses a convolution kernel-based photo-etching manufacturing and modelling method for integrated circuits. The present invention provides a photo-etching manufacturing simulation system frame based on a convolution kernel decomposition algorithm and uses a built convolution kernel group and the method of an established light intensity contribution table to reduce the calculation amount of space point light intensity greatly, and the distribution of silicon surface point light intensity in a photo-etching manufacturing process for integrated circuits can be calculated and predicted quickly. Thereby, the present invention can be used for the quick extraction of two-dimensional imaging contours in photo-etching simulation and can be applied to the verification of the manufacturability the design for integrated circuits.

Description

A kind of modeling method for integrated circuit photolithography manufacturing based on convolution kernel

Technical field

The present invention relates to the integrated circuit (IC) etching analogy method,, belong to the integrated circuit CAD field especially based on the modeling method for integrated circuit photolithography manufacturing of convolution kernel.

Background technology

The minimum feature of integrated circuit and minimum spacing become more and more littler, when the characteristic dimension of exposure lines during near the theoretical resolving limit of exposure system, the silicon wafer surface imaging will produce significantly distortion, promptly produce so-called optical proximity effect (OPE, optical proximity effect), thus cause the litho pattern quality seriously to descend.Inconsistent between the actual print figure of any mask graph and silicon wafer surface, i.e. the distortion of IC domain figure transfer all can influence the performance parameter of final product, and reduces the rate that manufactures a finished product of integrated circuit.The original design that can meet domain for the result who makes photoetching best, industry member has proposed mask is made pre-distortion (OPC, optical proximity correction) or on mask, add the mask compensation methodes such as (PSM, phase-shifting mask) of one deck phase shift mould.The following grid technique of 0.18um of all important integrated circuit manufacturers has all used above-mentioned technology in the world at present.

Optical proximity correction (OPC) is a most important component in the mask compensation technique, be the design of present Deep Sub-Micron VLSI and produce in most important, the most frequently used mask compensation method, its ultimate principle is to change in advance that the shape of figure compensates because the non-linear caused distortion of optical diffraction and technology on the mask.After using this technology under the identical working condition, can produce with existing lithographic equipment and have the more integrated circuit of small-feature-size lines.And guide the use of OPC technology in order correctly to estimate imaging on the silicon chip under the condition of sub-wavelength lithography, the optical patterning simulation is indispensable in modern integrated circuits production.Along with the scale of integrated circuit near the gigabit level, often the data volume of one deck domain will reach GB, it must be rapidly and efficiently keeping under the same precision that this situation requires practical optical patterning simulation system.

The optical patterning problem of modelling can be expressed as the projection imaging problem of partially coherent light in the aperture system of zonal aberration to a great extent.In order to obtain the two-dimensional optical imaging result of mask under given optical system condition.Original optical patterning simulation system (as famous SPLAT) all is to calculate by the Hopkins formula in the Fourier optics:

$I(f,g)={\∫}_{-\∞}^{+\∞}{\∫}_{-\∞}^{+\∞}T(f^{\′}+f,g^{\′}+g;f^{\′},g^{\′})\·F(f^{\′}+f,g^{\′}+g)\·F^H(f^{\′},g^{\′})d{f}^{\′}d{g}^{\′}---\left(a\right)$

I(x，y)＝F ^-1{I(f，g)} (b)

Wherein I (f, g) be output intensity I (x, two-dimensional Fourier transform y), F (f, g) be mask transition function F (x, two-dimensional Fourier transform y), T (f ', g '; F "; g ") be the transmission interaction coefficent (TCC of optical system, transmission cross coefficient), it is a four-dimensional function that has nothing to do fully with mask shape, described from light source to the effect as the whole optical system that comprises illuminator and imaging system the plane, its expression formula is:

$T(f^{\′},g^{\′};f^{\′\′},g^{\′\′})={\∫}_{-\∞}^{+\∞}{\∫}_{-\∞}^{+\∞}J(f,g)\·K(f+f^{\′},g+g^{\′})\·K^H(f+f^{\′\′},g+g^{\′\′})\mathrm{dfdg}---\left(c\right)$

Wherein (f g) is the interaural crosscorrelation function of light source to J; (f g) is the frequency response function of imaging system to K.

Because the Hopkins formula is a nonlinear system in essence, for calculating the light distribution in a zone, must calculate one time 4 repeated integral and comprise the FFT of several times, calculated amount is quite big.Along with the scale of integrated circuit near the gigabit level, often the data volume of one deck domain will reach GB, if simulation system is still carried out simulation to the optical patterning system according to original Hopkins formula, the travelling speed of total system will must not have practicality (it is generally acknowledged that so this method is practical if the single treatment process can be finished in 24 hours) slowly.Therefore, realize the imperative at last task of spatial point light intensity meter fast.

Summary of the invention

The objective of the invention is to propose a kind of modeling method for integrated circuit photolithography manufacturing, to realize comparatively accurately and to predict integrated circuit optical patterning result fast based on convolution kernel.

Modeling method for integrated circuit photolithography manufacturing based on convolution kernel of the present invention in turn includes the following steps:

1) is provided with

The basic parameter of litho machine: the wavelength X of light source, the numerical aperture NA of optical system, the coefficient of coherence s of illumination, the thing of optical system/as enlargement ratio M, the spacial influence scope A of etching system;

2) calculate light source interaural crosscorrelation function J (f, g)

According to the light source form and the position of photo-etching machine illumination system, utilize the 667th page to 677 pages described formula in Science Press 1981 version " optical principle ", calculate light source interaural crosscorrelation function J (f, the g) distribution on frequency domain, f wherein, g is the frequency domain coordinate;

3) calculate imaging system frequency response function K (f, g)

Pupil according to the litho machine imaging system differs parameter, utilizes the 616th page to 634 pages described formula in Science Press 1981 version " optical principle ", calculate imaging system frequency response function K (f, the g) distribution on frequency domain, f wherein, g is the frequency domain coordinate;

4) make up the 4 transmission interaction coefficent TCC that tie up

Calculate the TCC matrix by following formula, f ' wherein, g ', f ", g ", f, g are the frequency domain coordinate:

$T(f^{\′},g^{\′};f^{\′\′},g^{\′\′})={\∫}_{-\∞}^{+\∞}{\∫}_{-\∞}^{+\∞}J(f,g)\·K(f+f^{\′},g+g^{\′})\·K^H(f+f^{\′\′},g+g^{\′\′})\mathrm{dfdg}---\left(1\right)$

5) parameter of calibration model

Read in the test domain that is used to proofread and correct lithography model, read in the measured data after this domain is made through litho machine, calculate the test domain through the simulation photoetching after the size of figure, and compare with measured data, calculate the error ε of simulation process by following formula _Total:

${\mathrm{\ϵ}}_{\mathrm{total}}=\sqrt{\underset{i}{\mathrm{\Σ}}{(d_{\mathrm{mode}\mathrm{li}}-d_{\mathrm{measurei}})}^2}---\left(2\right)$

D wherein _ModeliThe size of representing i analog computation, d _MeasureiThe size of i actual measurement;

Change λ one by one, NA, s, and the pupil of imaging system differs parameter, recomputates the transmission interaction coefficent TCC of 4 dimensions, and repeat the error ε that said process calculates simulation process _Total

Choose ε _TotalThis minimum group model parameter is as the parameter of proofreading and correct the back model, and the transmission interaction coefficent of this moment is for proofreading and correct the transmission interaction coefficent of back model;

6) arrange the TCC matrix with two-dimensional approach

The definition (f1, g1) and (f2 g2) is respectively new row matrix, column number, and TCC is arranged with two-dimensional approach, is shown below:

$\mathrm{TCC}(\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">f</figure-callout>}1,\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">g</figure-callout>}1,f2,g2)=\left[\begin{array}{ccc}{\mathrm{Tcc}}_{\mathrm{0,0,0,0}}& \mathrm{\&Lambda;}& {\mathrm{Tcc}}_{\mathrm{0,0},f2,g2}\\ M& O& \mathrm{<figure-callout\; id="1"\; label="M\; Tcc\; f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">M</figure-callout>}& \\ {\mathrm{Tcc}}_f{1,\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">g</figure-callout>}\mathrm{1,0,0}}_{}& \mathrm{\&Lambda;}& {\mathrm{<figure-callout\; id="1"\; label="Tcc\; f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">Tcc</figure-callout>}}_f\end{array}\right]---\left(3\right)$

7) decompose the TCC matrix

Calculate the eigen vector of TCC matrix through the following steps:

The first step by orthogonal transformation symmetrical tridiagonal matrix of reality of TCC matrix boil down to;

Second step was obtained the eigenwert and the proper vector of this condensation matrix;

Proper vector and the first step used orthogonal matrix of the 3rd step with condensation matrix multiplies each other, and obtains the proper vector of TCC matrix;

8) select Partial Feature vector sum eigenwert group to constitute spatial convoluted nuclear group

Eigenwert is sorted by size, and selects maximum at least 6 eigenwerts and characteristic of correspondence vector thereof to form spatial convoluted nuclear group, to the proper vector chosen with f for row-coordinate g carries out permutatation for the row coordinate, obtain the matrix form of convolution kernel;

9) set up the light intensity question blank

By following formula each element pattern is calculated light intensity value, and be arranged in table, wherein K _i(j k) is i convolution kernel, F (j k) is the fourier spectrum of element pattern,

$I_i(j,k)=\underset{j=0}{\overset{J}{\mathrm{\&Sigma;}}}\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}{K}_i(j,k)\&CircleTimes;F(j,k)---\left(4\right)$

Modeling method for integrated circuit photolithography manufacturing based on convolution kernel of the present invention has following advantage:

(1) can comparatively calculate to a nicety the domain figure through the profile behind the optical patterning;

(2) computing velocity is very fast, and can handle large-scale integrated circuit diagram;

(3) can be advantageously applied to the manufacturability checking of integrated circuit (IC) design under the sub wavelength light etching condition and the OPC of domain proofreaies and correct.

Description of drawings

Fig. 1 is a process flow diagram of the present invention;

Fig. 2 is the model tuning process flow diagram;

Fig. 3 sets up convolution kernel group process flow diagram;

Fig. 4 sets up light intensity question blank process flow diagram;

Fig. 5 is by light intensity question blank centering point light intensity synoptic diagram.

Embodiment

Adopt the program circuit explanation the present invention of typical data now in conjunction with Fig. 1:

1) is provided with

The basic parameter of litho machine: the wavelength X of light source=0.248, the numerical aperture NA=0.85 of optical system, the coefficient of coherence s=0.75 of illumination, the thing of optical system/as enlargement ratio M=1/5, the spacial influence scope A of etching system, as establish A=1024nm, can think that so on mask decentering point distance can not exert an influence greater than the figure at the 1024nm place light intensity to central point.

2) calculate light source interaural crosscorrelation function J (f, g)

According to the light source form and the position of photo-etching machine illumination system, calculate interaural crosscorrelation function J (f, g) distribution on frequency domain of light source.With traditional circular illumination is example, utilize time institute's setting parameter is set, J (f, g) calculate by following formula:

$J(f,g)=\left\{\begin{array}{cc}\frac{{\mathrm{\&lambda;}}^2}{\mathrm{\&pi;}\&CenterDot;s^2\&CenterDot;{\mathrm{NA}}^2}& f^2+g^2<{\left(\frac{s\&CenterDot;\mathrm{NA}}{\mathrm{\&lambda;}}\right)}^2\\ 0& f^2+g^2\&GreaterEqual;{\left(\frac{s\&CenterDot;\mathrm{NA}}{\mathrm{\&lambda;}}\right)}^2\end{array}\right.$

Following distribution is arranged:

$J(f,g)=\left\{\begin{array}{cc}0.4754& f^2+g^2<6.6078\\ 0& f^2+g^2\&GreaterEqual;6.6078\end{array}\right.$

3) calculate imaging system frequency response function K (f, g)

(f, g) the focusing situation of defective that exists with imaging system and imaging is relevant, differs parameter (out of focus, spherical aberration, coma etc.) according to the pupil of litho machine imaging system, calculates frequency response function K (f, g) distribution on frequency domain of imaging system for K.For example establishing the thing of optical system/as enlargement ratio is 5: 1, and other differs parameter and be at 0 o'clock, calculates by following formula:

$K(f,g)=\left\{\begin{array}{cc}P(f,g)& f^2+g^2<{\left(\frac{\mathrm{NA}}{\mathrm{\&lambda;}\&CenterDot;M}\right)}^2\\ 0& f^2+g^2\&GreaterEqual;{\left(\frac{\mathrm{NA}}{\mathrm{\&lambda;}\&CenterDot;M}\right)}^2\end{array}\right.$

Wherein (f g) is pupil function to P, and when differing parameter when being 0, (f, g) perseverance is 1 to P.

K (f g) has following distribution:

$K(f,g)=\left\{\begin{array}{cc}1& f^2+g^2<283.68\\ 0& f^2+g^2\&GreaterEqual;283.68\end{array}\right.$

4) make up the 4 transmission interaction coefficent TCC that tie up

The discrete form of calculating following formula can obtain describing from light source to the transmission interaction coefficent TCC as the effect of the whole optical system that comprises illuminator and imaging system the plane, and under the situation of discretize, TCC is the matrix of a four-dimension:

$T(f^{\&prime;},g^{\&prime;};f^{\&prime;\&prime;},g^{\&prime;\&prime;})={\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}J(f,g)\&CenterDot;K(f+f^{\&prime;},g+g^{\&prime;})\&CenterDot;K^H(f+f^{\&prime;\&prime;},g+g^{\&prime;\&prime;})\mathrm{dfdg}---\left(1\right)$

5) parameter of calibration model

Because the systematic error that model itself exists and the measuring error of each input parameter can not be described actual etching system the most accurately by the model that abovementioned steps is set up, and must just can obtain reasonable result by the correction with measured data.The visible Fig. 2 of model tuning flow process.The method of the statistical model error of calculation is as follows among the figure:

Read in the test domain that is used to proofread and correct lithography model, read in the measured data after this domain is made through litho machine, calculate the test domain through the simulation photoetching after the size of figure, and compare with measured data, calculate the error ε of simulation process by following formula _Total:

${\mathrm{\&epsiv;}}_{\mathrm{total}}=\sqrt{\underset{i}{\mathrm{\&Sigma;}}{(d_{\mathrm{mode}\mathrm{li}}-d_{\mathrm{measurei}})}^2}---\left(2\right)$

D wherein _ModeliThe size of representing i analog computation, d _MeasureiThe size of i actual measurement;

Change λ one by one, NA, s, and the pupil of imaging system differs parameter, recomputates the transmission interaction coefficent TCC of 4 dimensions, and repeat the error ε that said process calculates simulation process _Total

Choose ε _TotalThis minimum group model parameter is as the parameter of proofreading and correct the back model, and the transmission interaction coefficent of this moment is for proofreading and correct the transmission interaction coefficent of back model.

6) arrange the TCC matrix with two-dimensional approach

The definition (f1, g1) and (f2 g2) is respectively new row matrix column number, and TCC is arranged with two-dimensional approach, is shown below:

$\mathrm{TCC}(\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">f</figure-callout>}1,\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">g</figure-callout>}1,f2,g2)=\left[\begin{array}{ccc}{\mathrm{Tcc}}_{\mathrm{0,0,0,0}}& \mathrm{\&Lambda;}& {\mathrm{Tcc}}_{\mathrm{0,0},f2,g2}\\ M& O& \mathrm{<figure-callout\; id="1"\; label="M\; Tcc\; f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">M</figure-callout>}& \\ {\mathrm{Tcc}}_f{1,\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">g</figure-callout>}\mathrm{1,0,0}}_{}& \mathrm{\&Lambda;}& {\mathrm{<figure-callout\; id="1"\; label="Tcc\; f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">Tcc</figure-callout>}}_f\end{array}\right]---\left(3\right)$

7) decompose the TCC matrix

The transmission interaction coefficent TCC of optical imaging system is the function of a four-dimension, and convolution kernel is the function of bidimensional.Usually the system function that uses in optical analogy is the TCC after the discretize, and it is the matrix of a four-dimension, and convolution kernel then is the matrix of bidimensional.Relation between them is shown below:

$\mathrm{TCC}[\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">f</figure-callout>}1,\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">g</figure-callout>}1,f2,g2]=\underset{i}{\mathrm{\&Sigma;}}{K}_i[\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">f</figure-callout>}1,g1]\&times;K_i{[f2,g2]}^H---\left(i\right)$

Promptly $\left[\begin{array}{ccc}{\mathrm{Tcc}}_{\mathrm{0,0,0,0}}& \mathrm{\&Lambda;}& {\mathrm{Tcc}}_{\mathrm{0,0},f2,g2}\\ M& O& \mathrm{<figure-callout\; id="1"\; label="M\; Tcc\; f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">M</figure-callout>}& \\ {\mathrm{Tcc}}_f{1,\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">g</figure-callout>}\mathrm{1,0,0}}_{}& \mathrm{\&Lambda;}& {\mathrm{<figure-callout\; id="1"\; label="Tcc\; f"\; filenames="C20051006076000142.png"\; state="\{\{state\}\}">Tcc</figure-callout>}}_f\end{array}\right]=M\&times;M^H---\left(\mathrm{ii}\right)$

Wherein matrix M is:

$M=\left[\begin{array}{ccc}{K}_0\left(\mathrm{0,0}\right)& \mathrm{\&Lambda;}& K_m\left(\mathrm{0,0}\right)\\ M& O& M\\ K_0(f,g)& \mathrm{\&Lambda;}& K_m(f,g)\end{array}\right]---\left(\mathrm{iii}\right)$

Because the quadrature decomposed form of TCC matrix is TCC=U * Λ * U ^H, with formula (ii) more as can be known:

$M=\left[\begin{array}{ccc}{K}_0\left(\mathrm{0,0}\right)& \mathrm{\&Lambda;}& K_m\left(\mathrm{0,0}\right)\\ M& O& M\\ K_0(f,g)& \mathrm{\&Lambda;}& K_m(f,g)\end{array}\right]=\left[\begin{array}{ccc}{V}_0\left(\mathrm{0,0}\right)& \mathrm{\&Lambda;}& V_m\left(\mathrm{0,0}\right)\\ M& O& M\\ V_0(f,g)& \mathrm{\&Lambda;}& V_m(f,g)\end{array}\right]\&times;\sqrt{\left[\begin{array}{ccc}\sqrt{{\mathrm{\&lambda;}}_0}& \mathrm{\&Lambda;}& 0\\ M& O& M\\ 0& \mathrm{\&Lambda;}& \sqrt{{\mathrm{\&lambda;}}_m}\end{array}\right]}---\left(\mathrm{iv}\right)$

Promptly $K_i(f,g)=V_i(f,g)\&times;\sqrt{{\mathrm{\&lambda;}}_i},$ V wherein _i(f, g) and λ _iIt is TCC matrix character pair vector sum eigenwert.

Simultaneously because the symmetry that formula (1) itself exists is Hermitian (Hermitian) matrix, i.e. TCC=TCC after TCC arranges as stated above ^H(H is a conjugate transpose).The process of finding the solution convolution kernel like this just is converted into the proper vector of asking hermitian matrix and the problem of eigenwert.

After obtaining the TCC that arranges with two-dimensional matrix, calculate the eigen vector of TCC matrix through the following steps:

The first step by orthogonal transformation symmetrical tridiagonal matrix of reality of TCC matrix boil down to;

Second step was obtained the eigenwert and the proper vector of this condensation matrix;

Proper vector and the first step used orthogonal matrix of the 3rd step with condensation matrix multiplies each other, and obtains the proper vector of TCC matrix.

8) select Partial Feature vector sum eigenwert group to constitute spatial convoluted nuclear group

For example to obtaining following eigenwert after certain TCC matrix decomposition: [57.26133 6.436457 6.436457 1.199264 1.198962 1.011634 0.000263 0.000263 ... ], in this example since the 7th eigenwert numerical value all much smaller than 1, promptly final light distribution is had only less influence, can reach certain precision so choose preceding 6 convolution kernels formation convolution kernel group since the 7th convolution kernel and convolution kernel afterwards thereof.

Since by TCC decompose the proper vector obtain all be (f, g) for row coordinate numbering, need to the proper vector chosen with f for row-coordinate g for the row coordinate carries out permutatation, obtain the matrix form of convolution kernel.Set up convolution kernel group process flow diagram and see Fig. 3.

9) set up the light intensity question blank

The light intensity question blank is to set up on the basis of spatial convoluted nuclear.The input of question blank is the domain image relevant with a light intensity, and output is the contribution of this part domain image to a light intensity.By following formula each element pattern is calculated light intensity value, wherein K _i(j k) is i convolution kernel, F (j k) is the fourier spectrum of element pattern,

$I_i(j,k)=\underset{j=0}{\overset{J}{\mathrm{\&Sigma;}}}\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}{K}_i(j,k)\&CircleTimes;F(j,k)---\left(4\right)$

Question blank is set up at each convolution kernel and each element pattern, referring to Fig. 4.The shape of element pattern generally has 3 kinds, promptly among Fig. 41,2, shown in 3.For example for aforementioned lights etching system coverage A=1024nm, the domain minimum dimension is the situation of 1nm, must be at x, and the y direction is that step-length is each combination calculation light intensity contribution with 1nm from-1024nm to 1024nm, will calculate 2048 * 2048 points here altogether.3 kinds of element patterns, and 6 convolution kernels are arranged, therefore need calculate altogether 3 * 6 * 2048 * 2048 times in this example, obtain 3 * 6 question blanks.Each calculating all is that convolution kernel and element pattern are made convolution algorithm and obtained the central points value.

Through the model that above-mentioned steps makes up, the distribution that can calculate any domain light intensity by following method:

On domain, determine to need to calculate the point of light intensity, calculate every some light intensity successively.At first isolate on every side the contributive graphics field of this light intensity, as shown in Figure 5, the spatial dimension of frame of broken lines representation model among the figure, solid box region representation lithography layout figure.Then figure is resolved into the combination of element pattern, then utilize question blank, each element pattern is found out its light intensity contribution to central point, at last the light intensity contribution summation of all element patterns is promptly obtained the light intensity value of central point.

Claims (1)

1. modeling method for integrated circuit photolithography manufacturing based on convolution kernel is characterized in that it in turn includes the following steps:

1) is provided with

The basic parameter of litho machine: the wavelength X of light source, the numerical aperture NA of optical system, the coefficient of coherence s of illumination, the thing of optical system/as enlargement ratio M, the spacial influence scope A of etching system;

2) calculate light source interaural crosscorrelation function J (f, g)

According to the light source form and the position of photo-etching machine illumination system, calculate light source interaural crosscorrelation function J (f, the g) distribution on frequency domain, f wherein, g is the frequency domain coordinate;

3) calculate imaging system frequency response function K (f, g)

Pupil according to the litho machine imaging system differs parameter, calculate imaging system frequency response function K (f, the g) distribution on frequency domain, f wherein, g is the frequency domain coordinate;

4) make up the 4 transmission interaction coefficent TCC that tie up

Calculate transmission interaction coefficent TCC matrix by following formula, f ' wherein, g ', f ", g ", f, g are the frequency domain coordinate,

$T(f^{\&prime;},g^{\&prime;};f^{\&prime;\&prime;},g^{\&prime;\&prime;})={\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}J(f,g)\&CenterDot;K(f+f^{\&prime;},g+g^{\&prime;})\&CenterDot;K^H(f+f^{\&prime;\&prime;},g+g^{\&prime;\&prime;})\mathrm{dfdg}$

------------(1)

5) parameter of calibration model

Read in the test domain that is used to proofread and correct lithography model, read in the measured data after this domain is made through litho machine, calculate the test domain through the simulation photoetching after the size of figure, and compare with measured data, calculate the error ε of simulation process by following formula _Total:

${\mathrm{\&epsiv;}}_{\mathrm{total}}=\sqrt{\underset{i}{\mathrm{\&Sigma;}}{(d_{\mathrm{mod}\mathrm{eli}}-d_{\mathrm{measurei}})}^2}$

------------(2)

D wherein _{Mod eli}The size of representing i analog computation, d _MeasureiThe size of i actual measurement;

Change λ one by one, NA, s, and the pupil of imaging system differs parameter, recomputates the transmission interaction coefficent TCC of 4 dimensions, and repeat the error ε that said process calculates simulation process _Total

Choose ε _TotalThis minimum group model parameter is as the parameter of proofreading and correct the back model, and the transmission interaction coefficent of this moment is for proofreading and correct the transmission interaction coefficent of back model;

6) arrange transmission interaction coefficent TCC matrix with two-dimensional approach

Definition (f1, g1) and (f2 g2) is respectively new row matrix column number, arranges with two-dimensional approach transmitting interaction coefficent TCC, is shown below:

$\mathrm{TCC}(f1,g1,f2,g2)=\left[\begin{array}{ccc}{\mathrm{Tcc}}_{\mathrm{0,0,0,0}}& \mathrm{\&Lambda;}& {\mathrm{Tcc}}_{\mathrm{0,0},f2,g2}\\ M& O& M\\ {\mathrm{Tcc}}_{f1,g\mathrm{1,0,0}}& \mathrm{\&Lambda;}& {\mathrm{Tcc}}_{f1,g1,f2,g2}\end{array}\right]$

------------(3)

7) decompose transmission interaction coefficent TCC matrix

Calculate the eigen vector of transmission interaction coefficent TCC matrix through the following steps:

The first step is by symmetrical tridiagonal matrix of reality of orthogonal transformation handle transmission interaction coefficent TCC matrix boil down to;

Second step was obtained the eigenwert and the proper vector of this condensation matrix;

Proper vector and the first step used orthogonal matrix of the 3rd step with condensation matrix multiplies each other, and obtains transmitting the proper vector of interaction coefficent TCC matrix;

8) select Partial Feature vector sum eigenwert group to constitute spatial convoluted nuclear group

Eigenwert is sorted by size, and selects maximum at least 6 eigenwerts and characteristic of correspondence vector thereof to form spatial convoluted nuclear group, to the proper vector chosen with f for row-coordinate g carries out permutatation for the row coordinate, obtain the matrix form of convolution kernel;

9) set up the light intensity question blank

By following formula each element pattern is calculated light intensity value, and be arranged in table, wherein K _i(j k) is i convolution kernel, F (j k) is the fourier spectrum of element pattern,

$I_i(j,k)=\underset{j=0}{\overset{J}{\mathrm{\&Sigma;}}}\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}{K}_i(j,k)\&CircleTimes;F(j,k)$

------------(4)。

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