CN102707563B - Light source and mask alternate optimization method based on Abbe vector imaging model - Google Patents

Abstract

The invention provides a light source and mask alternate optimization method based on an Abbe vector imaging model. According to the method, a graphics pixel value of a light source and transmissivity of an opening part and a light resistance part in a mask are set; variable matrixes omegaS and omegaM are established; a target function D is constructed to be a square of an Euler distance between a target graphics and an image in photoresist corresponding to the conventional light source and the conventional mask; and the alternate optimization process of the light source graphics and the mask graphics is guided according to the variable matrixes omegaS and omegaM and the target function D. Compared with the conventional method for independently optimizing the light source or the mask and synchronously optimizing the light source and the mask, the method has the advantage that the resolution of a photoetching system is effectively improved. Furthermore, the light source and the mask which are optimized by the method are applicable to small numerical apertures (NA) and NA which is more than 0.6. Moreover, according to gradient information of the optimized target function and a steepest speed reduction method, the efficiency for optimizing the light source graphics and the mask graphics is high.

Description

A kind of light source-mask based on Abbe vector imaging model replaces optimization method

Technical field

The present invention relates to a kind of light source-mask based on Abbe (Abbe) vector imaging model and replace optimization method, belong to photoetching resolution and strengthen technical field.

Background technology

Current large scale integrated circuit generally adopts etching system manufactured.Etching system mainly comprises: illuminator (comprising light source and condenser), mask, optical projection system and wafer four parts.The light that light source sends is incident to mask, the opening portion printing opacity of mask after condenser focuses on; After mask, light is incident on the wafer that scribbles photoresist via optical projection system, and mask graph just is replicated on wafer like this.

The etching system of main flow is the ArF degree of depth ultraviolet photolithographic system of 193nm at present, and along with the photoetching technique node enters 45nm-22nm, the critical size of circuit has been far smaller than the wavelength of light source.Therefore interference of light and diffraction phenomena are more remarkable, cause optical patterning to produce distortion and fuzzy.Etching system must adopt resolution enhance technology for this reason, in order to improve image quality.Light source-mask cooperate optimization (source mask optimization is called for short SMO) is a kind of important photoetching resolution enhancing technology.SMO utilizes the interaction between light source and mask, and the method by changing light source shading graphic, mask graph and add tiny auxiliary pattern on mask, reach the purpose that improves optical patterning resolution.Than traditional resolution enhance technology (as optical proximity correction (optical proximity correction, be called for short OPC) etc.), SMO introduces the light source variable in the photomask optimization process, increased the optimization degree of freedom, thus resolution that can more efficiently raising etching system.It is one of important method realized SMO that light source-mask is alternately optimized (sequential source mask optimization is called for short SESMO) method.The SESMO method is followed: optimize separately-light source of optimize separately-mask of light source is optimized separately ... order, what replace carries out independent optimization to light source and mask.Be characterized in Optimized Iterative each time, keep the constant more new light sources pixel value of mask pixels value, or keep the constant renewal mask pixels of light source pixel value value.

On the other hand, in order further to improve the etching system imaging resolution, industry generally adopts immersion lithographic system at present.Immersion lithographic system, between the lower surface at last lens of projection objective and wafer, having added the liquid that refractive index is greater than 1, enlarges numerical aperture (numerical aperture is called for short NA) thereby reach, and improves the purpose of imaging resolution.Because immersion lithographic system has the characteristic of high NA (NA>1), and when NA>0.6, the vector imaging characteristic of electromagnetic field can not be out in the cold on the impact of optical patterning, therefore no longer applicable for its scalar imaging model of immersion lithographic system.In order to obtain the imaging characteristic of accurate immersion lithographic system, must adopt the SMO technology based on the vector imaging model, the light source in immersion lithographic system and mask are optimized.

Pertinent literature (IEEE Transaction on Image Processing, 2011,20:2856～2864), for the partial coherence imaging system, has proposed a kind of SESMO optimization method based on gradient comparatively efficiently.Therefore but the scalar imaging model of above method based on etching system, be not suitable for the etching system of high NA.Simultaneously, due to the incident angle difference of diverse location light on surface of light source, its effect to optical projection system there are differences, but prior art is not considered the response difference of optical projection system to difference light source incident ray on surface of light source.Therefore adopt existing method to obtain aerial image and the larger deviation of physical presence, and then affect the effect of optimization of SESMO method.

Prior art discloses a kind of phase shift mask optimization method based on Abbe vector imaging model, and publication number is: CN102269925A.

Summary of the invention

The purpose of this invention is to provide a kind of SESMO method based on Abbe vector imaging model.The method adopts the SESMO technology based on vector model to be optimized light source shading graphic and mask graph, and it can be applicable to the dry lithography system that has the immersion lithographic system of high NA and have low NA simultaneously.

Realize that technical scheme of the present invention is as follows:

A kind of SESMO method based on Abbe vector imaging model, concrete steps are:

Step 101, light source is initialized as to size for N _S* N _SLight source figure J, it is the targeted graphical of N * N that mask graph M is initialized as to size

N wherein _SWith N be integer;

Step 102, the pixel value that the upper light-emitting zone of primary light source figure J is set are 1, and the pixel value of light-emitting zone is not 0; Set N _S* N _SMatrix of variables Ω _S: as J (x _s, y _s)=1 o'clock, As J (x _s, y _s)=0 o'clock,

J (x wherein _s, y _s) mean each pixel (x on the light source figure _s, y _s) pixel value; The transmissivity that initial mask figure M upper shed part is set is 1, and the transmissivity in resistance light zone is 0; Set the matrix of variables Ω of N * N _M: when M (x, y)=1,

When M (x, y)=0,

Wherein M (x, y) means the transmissivity of each pixel (x, y) on mask graph; Make two-value mask graph M _bInitial value be M;

Step 103, objective function D is configured to targeted graphical Euler's distance in the photoresist corresponding with current light source figure and mask graph between imaging square,

Wherein

For the pixel value of each pixel of targeted graphical, Z (x, y) means to utilize Abbe vector imaging model to calculate the pixel value of each pixel of imaging in current light source figure and photoresist corresponding to mask graph;

Step 104, calculating target function D are for matrix of variables Ω _SGradient matrix

Pixel value sum J by each pixel on the light source figure _sumBe approximately given constant, obtain gradient matrix

Approximate value

Utilize steepest prompt drop method to upgrade matrix of variables Ω _S, upgrade Ω _SFor

Wherein

For predefined light source Optimal Step Size, obtain corresponding current Ω _SLight source figure J, $J(x_s,y_s)=\frac{1}{2}[1+\cos {\mathrm{\Ω}}_S(x_s,y_s)];$

Step 105, calculating current light source figure J and two-value mask graph M _bThe value of corresponding target function value D; When this value is less than predetermined threshold or upgrades matrix of variables Ω _SNumber of times reach predetermined upper limit value K _SThe time, enter step 106, otherwise return to step 104;

Step 106, calculating target function D are for matrix of variables Ω _MGradient matrix

Utilize steepest prompt drop method to upgrade matrix of variables Ω _M, upgrade Ω _MFor

Wherein For predefined photomask optimization step-length, obtain corresponding current Ω _MMask graph M,

Upgrade the two-value mask graph M of corresponding current M _b,

T generally _m=0.5;

Step 107, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or upgrades matrix of variables Ω _MNumber of times reach predetermined upper limit value K _MThe time, enter step 108, otherwise return to step 106;

Step 108, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or alternately upgrades matrix of variables Ω _SAnd Ω _MNumber of times reach predetermined upper limit value K _S-MThe time, enter step 109, otherwise return to step 104;

Step 109, stop optimizing, and by current light source figure J and two-value mask graph M _bBe defined as light source figure and mask graph after optimizing.

In step 103 of the present invention, utilize the concrete steps of imaging in the photoresist that Abbe vector imaging model calculating current light source and mask are corresponding to be:

Step 201, mask graph M grid is turned to N * N sub regions;

Step 202, light source figure J grid is turned to N _S* N _SSub regions;

Step 203, for a single point light source (x _s, y _s), the aerial image I (x while obtaining this spot light on corresponding wafer position _s, y _s);

Step 204, judge whether to calculate the aerial image on the corresponding wafer positions of all pointolites, if enter step 205, otherwise return to step 203;

Step 205, according to Abbe Abbe method, to the aerial image I (x on the corresponding wafer position of each pointolite _s, y _s) superposeed, while obtaining the partial coherence light illumination, the aerial image I on wafer position;

Step 206, based on the photoresist approximate model, calculate the imaging in light source figure and photoresist corresponding to mask graph according to aerial image I.

In step 203 of the present invention for a single point light source (x _s, y _s), the aerial image I (x while obtaining this spot light on corresponding wafer position _s, y _s) detailed process be:

The direction of setting optical axis is the z axle, and sets up global coordinate system according to the left-handed coordinate system principle;

Step 301, according to pointolite coordinate (x _s, y _s), the near field distribution E of the light wave that the calculation level light source sends N * N sub regions on mask; Wherein, the vector matrix that E is N * N, its each element is one 3 * 1 vector, means 3 components of the diffraction near field distribution of mask in global coordinate system;

Step 302, according near field distribution E, obtain the Electric Field Distribution of light wave at optical projection system entrance pupil rear

Wherein,

For the vector matrix of N * N, its each element is one 3 * 1 vector, means 3 components of the Electric Field Distribution at entrance pupil rear in global coordinate system;

Step 303, to establish light wave direction of propagation in optical projection system approximate parallel with optical axis, further according to the Electric Field Distribution at entrance pupil rear

Obtain the Electric Field Distribution in optical projection system emergent pupil the place ahead

Wherein, the Electric Field Distribution in emergent pupil the place ahead

For the vector matrix of N * N, its each element is one 3 * 1 vector, means 3 components of the Electric Field Distribution in emergent pupil the place ahead in global coordinate system;

Step 304, according to the Electric Field Distribution in optical projection system emergent pupil the place ahead

Obtain the Electric Field Distribution at optical projection system emergent pupil rear

Step 305, utilize Wolf Wolf optical imagery theory, according to the Electric Field Distribution at emergent pupil rear

Obtain the Electric Field Distribution E on wafer ^Wafer, and according to E ^WaferAerial image I (x on the corresponding wafer position of acquisition point light source _s, y _s).

Beneficial effect

Than the independent optimization method of traditional light source and the independent optimization method of mask, the SESMO method the present invention relates to is utilized the interaction between light source and mask, introduce the light source variable in the photomask optimization process, increased the optimization degree of freedom, thus resolution that can more efficiently raising etching system.Synchronously optimize (simultaneous source mask optimization than light source-mask, be called for short SISMO) method, the SESMO method the present invention relates to can be by alternately optimizing light source and mask, effectively reduce the probability that optimized algorithm is absorbed in local optimum, thereby can access the optimum results that more approaches global optimum, and the resolution of more efficiently raising etching system.

Secondly, the present invention utilizes Abbe vector imaging model to describe the imaging process of etching system, has considered the vectorial property of electromagnetic field, and the light source figure after optimization and mask graph not only are applicable to the situation of little NA, also are applicable to the situation of NA>0.6.

Again, the present invention utilizes the gradient information of optimization aim function, in conjunction with steepest prompt drop method, light source figure and mask graph is optimized, and optimization efficiency is high.

Finally, the present invention is tiled into a plurality of pointolites by surface of light source, for the difference light source, calculates respectively its corresponding aerial image, has advantages of that degree of accuracy is high, the method is applicable to difform light source, and meets the lithography simulation demand of 45nm and following technology node.

The accompanying drawing explanation

Fig. 1 is the process flow diagram that the present invention is based on the SESMO method of Abbe vector imaging model.

Fig. 2 is that pointolite sends light wave form the schematic diagram of aerial image after mask, optical projection system on wafer position.

The schematic diagram of imaging in the photoresist that Fig. 3 is primary light source, initial mask and correspondence thereof.

The schematic diagram of imaging in the photoresist that Fig. 4 is the independent optimum results of light source, initial mask figure and correspondence thereof based on Abbe vector imaging model.

Fig. 5 is the primary light source figure, the schematic diagram of imaging in the independent optimum results of mask based on Abbe vector imaging model and corresponding photoresist thereof.

The schematic diagram of imaging in the photoresist of Fig. 6 light source figure, mask graph and correspondence thereof after the SISMO method optimization based on Abbe vector imaging model for employing.

The schematic diagram of imaging in the photoresist of Fig. 7 light source figure, mask graph and correspondence thereof after the SESMO method optimization based on Abbe vector imaging model for employing.

Embodiment

Below in conjunction with accompanying drawing, further the present invention is described in detail.

Principle of the present invention: when light identical with targeted graphical or when approximate, the figure be printed in etching system on wafer has very high resolution by mask imaging in photoresist.Therefore the present invention by the optimization aim function D of SESMO be configured to the Euler's distance between imaging in the corresponding photoresist of targeted graphical and light source and mask square; As the size of targeted graphical is N * N,

For the pixel value of each point in targeted graphical, the pixel value that Z (x, y) is imaging in light source and the corresponding photoresist of mask, Z (x, y) with

Value be 0 or 1, the present invention means the position of this pixel with the centre coordinate of each pixel on figure or image.

As shown in Figure 1, the present invention is based on the SESMO method of Abbe vector imaging model, concrete steps are:

Step 101, light source is initialized as to size for N _S* N _SLight source figure J, it is the targeted graphical of N * N that mask graph M is initialized as to size

N wherein _SWith N be integer.

Step 102, the pixel value that the upper light-emitting zone of primary light source figure J is set are 1, and the pixel value of light-emitting zone is not 0; Set N _S* N _SMatrix of variables Ω _S: as J (x _s, y _s)=1 o'clock,

As J (x _s, y _s)=0 o'clock,

J (x wherein _s, y _s) mean each pixel (x on the light source figure _s, y _s) pixel value.The transmissivity that initial mask figure M upper shed part is set is 1, and the transmissivity in resistance light zone is 0; Set the matrix of variables Ω of N * N _M: when M (x, y)=1,

When M (x, y)=0,

Wherein M (x, y) means the transmissivity of each pixel (x, y) on mask graph; Make two-value mask graph M _bInitial value be M.

Step 103, by objective function D be configured to the Euler's distance between imaging in photoresist that targeted graphical is corresponding with current light source and mask square,

Wherein

For the pixel value of each pixel of targeted graphical, Z (x, y) means to utilize Abbe vector imaging model to calculate the pixel value of each pixel of imaging in current light source figure and photoresist corresponding to mask graph;

The concrete steps that the present invention utilizes Abbe vector imaging model to calculate imaging in current light source figure and the corresponding photoresist of mask graph are:

Variable predefine

As shown in Figure 2, the direction of setting optical axis is the z axle, and sets up global coordinate system (x, y, z) according to the left-handed coordinate system principle with the z axle; If on partial coherence light source face, the world coordinates of any point light source is (x _s, y _s, z _s), the direction cosine of being sent and be incident to the plane wave of mask by this pointolite are (α _s, β _s, γ _s), the pass between world coordinates and direction cosine is:

α _s＝x _s·NA _m，β _s＝y _s·NA _m， ${\mathrm{\γ}}_s=\cos \left[{\sin }^{-1}({\mathrm{NA}}_m\·\sqrt{x_s^2+y_s^2})\right]$

Wherein, NA _mFor optical projection system object space numerical aperture.

If on mask, the world coordinates of any point is (x, y, z), based on diffraction principle, the direction cosine that are incident to the plane wave of optical projection system entrance pupil from mask are (α, beta, gamma), (α wherein, β, γ) be the coordinate system after the upper global coordinate system (x, y, z) of mask (object plane) carries out Fourier transform.

If the world coordinates of the upper any point of wafer (image planes) is (x _w, y _w, z _w), the direction cosine that are incident to the plane wave of image planes from the optical projection system emergent pupil are (α ', β ', γ '), and wherein (α ', β ', γ ') be the upper global coordinate system (x of wafer (image planes) _w, y _w, z _w) carry out the coordinate system after Fourier transform.

Transformational relation between global coordinate system and local coordinate system:

Set up local coordinate system (e _⊥, e _||), e _⊥Axle is the emit beam direction of vibration of middle TE polarized light of light source, e _||Axle is the emit beam direction of vibration of middle TM polarized light of light source.Wave vector is The plane consisted of wave vector and optical axis is called the plane of incidence, and the direction of vibration of TM polarized light is in the plane of incidence, and the direction of vibration of TE polarized light is perpendicular to the plane of incidence.The transformational relation of global coordinate system and local coordinate system is:

$\left[\begin{array}{c}{E}_x\\ E_y\\ E_z\end{array}\right]=T\·\left[\begin{array}{c}{E}_{\⊥}\\ E_{\left|\right|}\end{array}\right]$

Wherein, E _x, E _yAnd E _zRespectively that light source sends the component of light wave electric field in global coordinate system, E _⊥And E _||Be that light source sends the component of light wave electric field in local coordinate system, transition matrix T is:

$T=\left[\begin{array}{cc}-\frac{\mathrm{\β}}{\mathrm{\ρ}}& -\frac{\mathrm{\α\γ}}{\mathrm{\ρ}}\\ \frac{\mathrm{\α}}{\mathrm{\ρ}}& -\frac{\mathrm{\β\γ}}{\mathrm{\ρ}}\\ 0& \mathrm{\ρ}\end{array}\right]$

Wherein, $\mathrm{\ρ}=\sqrt{{\mathrm{\α}}^2+{\mathrm{\β}}^2}.$

The concrete steps of obtaining the method for imaging in the photoresist that mask is corresponding are:

Step 201, mask graph M grid is turned to N * N sub regions.

Step 202, light source figure J grid is turned to N _S* N _SSub regions.

Step 203, for a single point light source (x _s, y _s), the aerial image I (x while obtaining this spot light on corresponding wafer position _s, y _s);

Step 204, judge whether to calculate the aerial image on the corresponding wafer positions of all pointolites, if enter step 205, otherwise return to step 203;

Step 205, according to Abbe Abbe method, to the aerial image I (x on the corresponding wafer position of each pointolite _s, y _s) superposeed, while obtaining the partial coherence light illumination, the aerial image I on wafer position;

Step 206, based on the photoresist approximate model, calculate the imaging in light source figure and photoresist corresponding to mask graph according to aerial image I.

Below to utilizing for a single point light source (x in step 203 _s, y _s) aerial image I (x while obtaining this spot light on corresponding wafer position _s, y _s) process be further elaborated:

Step 301, as shown in Fig. 2 2301, for a single point light source (x _s, y _s), the near field distribution E of the light wave that the calculation level light source sends N * N sub regions on mask.

Wherein, the vector matrix that E is N * N is (if all elements of a matrix is matrix or vector, be called vector matrix), each element in this vector matrix is the vector of 3 * 1, means 3 components of the diffraction near field distribution of mask in global coordinate system.

Mean that two matrix corresponding elements multiply each other.

Be the vector matrix of one N * N, each element is equal to

The representative point light source sends the electric field intensity of electric field in global coordinate system of light wave; The electric field that a pointolite on the partial coherence light source sends light wave as established is expressed as in local coordinate system

${\stackrel{\→}{E}}_i=\left[\begin{array}{c}{E}_{\⊥}\\ E_{\left|\right|}\end{array}\right]$

This electric field is expressed as in global coordinate system:

${{\stackrel{\→}{E}}_i}^{\′}=T\·{\stackrel{\→}{E}}_i$

The diffraction matrices B of mask is the scalar matrix (if all elements in matrix is scalar, being called scalar matrix) of one N * N, and approximate according to Hopkins (Thelma Hopkins), each element of B can be expressed as:

$B(m,n)=\exp \left(\frac{j2\mathrm{\π}{\mathrm{\β}}_{s}x}{\mathrm{\λ}}\right)\exp \left(\frac{j2\mathrm{\π}{\mathrm{\α}}_{s}y}{\mathrm{\λ}}\right)$

$=\exp \left(\frac{j2\mathrm{\πm}{y}_{s}N{A}_m\×\mathrm{pixel}}{\mathrm{\λ}}\right)\exp \left(\frac{j2\mathrm{\πn}{x}_s{\mathrm{NA}}_m\×\mathrm{pixel}}{\mathrm{\λ}}\right),$ m，n＝1，2，...，N

Wherein, pixel means the length of side of all subregion on mask graph.

Step 302, as shown in Fig. 2 2302, obtain the Electric Field Distribution of light wave at optical projection system entrance pupil rear according near field distribution E

The detailed process of this step is:

Because each subregion on mask can be regarded a secondary sub-light source as, the coordinate using the center of subregion as this subregion, according to the Fourier optics theory, can be expressed as the Electric Field Distribution in optical projection system entrance pupil the place ahead the function of α and β:

$E_l^{\mathrm{ent}}(\mathrm{\α},\mathrm{\β})=\frac{\mathrm{\γ}}{\mathrm{j\λ}}\frac{e^{-\mathrm{jkr}}}{r}F\left\{E\right\}---\left(2\right)$

Wherein, owing to there being N * N sub regions on mask, so the Electric Field Distribution in entrance pupil the place ahead

For the vector matrix of N * N, each element in this vector matrix is one 3 * 1 vector, means 3 components of the Electric Field Distribution in entrance pupil the place ahead in global coordinate system.F{} means Fourier transform, and r is the entrance pupil radius,

For wave number, λ is the wavelength that pointolite sends light wave, n _mFor the object space medium refraction index.

Because the reduction magnification of optical projection system is larger, be generally 4 times, now the numerical aperture of object space is less, causes entrance pupil the place ahead Electric Field Distribution

Axial component can ignore, so optical projection system entrance pupil the place ahead is identical with the Electric Field Distribution at entrance pupil rear,

$E_b^{\mathrm{ent}}(\mathrm{\α},\mathrm{\β})=E_l^{\mathrm{ent}}(\mathrm{\α},\mathrm{\β})=\frac{\mathrm{\γ}}{\mathrm{j\λ}}\frac{e^{-\mathrm{jkr}}}{r}F\left\{E\right\}---\left(3\right)$

Wherein, owing to there being N * N sub regions on mask, so the Electric Field Distribution at entrance pupil rear

For the vector matrix of N * N, each element in this matrix is one 3 * 1 vector, means 3 components of the Electric Field Distribution at entrance pupil rear in global coordinate system.

Step 303, as shown in Fig. 2 2303, establish light wave direction of propagation in optical projection system approximate parallel with optical axis, further according to the Electric Field Distribution at entrance pupil rear Obtain the Electric Field Distribution in optical projection system emergent pupil the place ahead $E_l^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′}).$

The detailed process of this step is:

For aberrationless preferred view system, the mapping process of entrance pupil rear and emergent pupil the place ahead Electric Field Distribution can be expressed as the form of a low-pass filter function and a modifying factor product, that is:

Wherein, the Electric Field Distribution in emergent pupil the place ahead For the vector matrix of N * N, each element in this vector matrix is one 3 * 1 vector, means 3 components of the Electric Field Distribution in emergent pupil the place ahead in global coordinate system; C is the constant correction factor, and the scalar matrix that low-pass filter function U is N * N means the limited receiving ability of the numerical aperture of optical projection system to diffraction spectrum, and the value in pupil inside is 1, and the value of pupil outside is 0, specifically is expressed as follows:

$U=\left\{\begin{array}{cc}1& \sqrt{f^2+g^2}\≤1\\ 0& \mathrm{elsewhere}\end{array}\right.,$

Wherein, (f, g) is normalized world coordinates on entrance pupil.

Constant correction factor c can be expressed as:

$c=\frac{r}{r^{\′}}\sqrt{\frac{{\mathrm{\γ}}^{\′}}{\mathrm{\γ}}}\frac{n_w}{R}$

Wherein, r and r ' are respectively optical projection system entrance pupil and emergent pupil radius, n _wFor the refractive index of etching system image space immersion liquid, the reduction magnification that R is the preferred view system, be generally 4.

Be parallel to optical axis because the direction of propagation of light wave between optical projection system entrance pupil and emergent pupil is approximate, and therefore for arbitrarily (α ', β '), the entrance pupil rear is identical with the phase differential between emergent pupil the place ahead.Owing to finally wanting poor can the ignoring of constant phase between solution room picture (being light distribution) so entrance pupil rear and emergent pupil the place ahead.The Electric Field Distribution that can obtain thus emergent pupil the place ahead is:

Step 304, as shown in Fig. 2 2304, according to the Electric Field Distribution in optical projection system emergent pupil the place ahead Obtain the Electric Field Distribution at optical projection system emergent pupil rear

According to the rotation effect of TM component between emergent pupil the place ahead and rear of electromagnetic field, to establish in global coordinate system, the forward and backward side's of emergent pupil electric field is expressed as: the vector matrix of N * N

With

With

Each element as follows:

$E_l^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n)={[E_{\mathrm{lx}}^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n);E_{\mathrm{ly}}^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n);E_{\mathrm{lz}}^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n)]}^T$

$E_b^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n)={[E_{\mathrm{bx}}^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n);E_{\mathrm{by}}^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n);E_{\mathrm{bz}}^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′},m,n)]}^T$

Wherein, m, n=1,2 ..., N, α '=cos φ ' sin θ ', β '=sin φ ' sin θ ', γ '=cos θ ', the optical projection system emergent pupil is incident to the direction cosine (wave vector) of the plane wave of image planes and is

φ ' and θ ' are respectively position angle and the elevations angle of wave vector,

With

Relational expression be:

Wherein, V is the vector matrix of a N * N, and each element is the matrix of 3 * 3:

$V(m,n)=\left[\begin{array}{ccc}{\cos \mathrm{\φ}}^{\′}& {-\sin \mathrm{\φ}}^{\′}& 0\\ {\sin \mathrm{\φ}}^{\′}& {\cos \mathrm{\φ}}^{\′}& 0\\ 0& 0& 1\end{array}\right]\·\left[\begin{array}{ccc}{\cos \mathrm{\θ}}^{\′}& 0& {\sin \mathrm{\θ}}^{\′}\\ 0& 0& 1\\ {-\sin \mathrm{\θ}}^{\′}& 0& {\cos \mathrm{\θ}}^{\′}\end{array}\right]\·\left[\begin{array}{ccc}{\cos \mathrm{\φ}}^{\′}& {\sin \mathrm{\φ}}^{\′}& 0\\ {-\sin \mathrm{\φ}}^{\′}& {\cos \mathrm{\φ}}^{\′}& 0\\ 0& 0& 1\end{array}\right]$

$=\left[\begin{array}{ccc}{\cos }^2{\mathrm{\φ}}^{\′}{\cos \mathrm{\θ}}^{\′}+{\sin }^2{\mathrm{\φ}}^{\′}& {\cos \mathrm{\φ}}^{\′}{\sin \mathrm{\φ}}^{\′}({\cos \mathrm{\θ}}^{\′}-1)& {\cos \mathrm{\φ}}^{\′}{\sin \mathrm{\θ}}^{\′}\\ {\cos \mathrm{\φ}}^{\′}{\sin \mathrm{\φ}}^{\′}({\cos \mathrm{\θ}}^{\′}-1)& {\sin }^2{\mathrm{\φ}}^{\′}{\cos \mathrm{\θ}}^{\′}+{\cos }^2{\mathrm{\φ}}^{\′}& {\sin \mathrm{\φ}}^{\′}{\sin \mathrm{\θ}}^{\′}\\ -{\cos \mathrm{\φ}}^{\′}{\sin \mathrm{\θ}}^{\′}& {-\sin \mathrm{\φ}}^{\′}{\sin \mathrm{\θ}}^{\′}& {\cos \mathrm{\θ}}^{\′}\end{array}\right]$

$=\left[\begin{array}{ccc}\frac{{\mathrm{\β}}^{\′2}+{\mathrm{\α}}^{\′2}{\mathrm{\γ}}^{\′}}{1-{\mathrm{\γ}}^{\′2}}& -\frac{{\mathrm{\α}}^{\′}{\mathrm{\β}}^{\′}}{1+{\mathrm{\γ}}^{\′}}& {\mathrm{\α}}^{\′}\\ -\frac{{\mathrm{\α}}^{\′}{\mathrm{\β}}^{\′}}{1+{\mathrm{\γ}}^{\′}}& \frac{{\mathrm{\α}}^{\′2}+{\mathrm{\β}}^{\′2}{\mathrm{\γ}}^{\′}}{1-{\mathrm{\γ}}^{\′2}}& {\mathrm{\β}}^{\′}\\ -{\mathrm{\α}}^{\′}& {-\mathrm{\β}}^{\′}& {\mathrm{\γ}}^{\′}\end{array}\right]m,n=\mathrm{1,2},...,N$

Step 305, as shown in Fig. 2 2305, utilize the optical imagery theory of Wolf, according to the Electric Field Distribution at emergent pupil rear

Obtain the Electric Field Distribution E on wafer ^WaferAs formula (7), and the aerial image I (x on the corresponding wafer position of further acquisition point light source _s, y _s).

$E^{\mathrm{wafer}}=\frac{2{\mathrm{\π\λr}}^{\′}}{{\mathrm{jn}}_w^2}{e}^{{\mathrm{jk}}^{\′}{r}^{\′}}{F}^{-1}\left\{\frac{1}{{\mathrm{\γ}}^{\′}}{E}_b^{\mathrm{ext}}\right\}---\left(7\right)$

Wherein, F ^-1{ } is inverse Fourier transform.In (5) and (6) formula substitutions (7) formula, and ignore the constant phase item, can obtain:

(1) formula is updated in (8) formula, can obtains pointolite (x _s, y _s) light distribution of image planes while throwing light on, that is:

Due to E _i' middle element value and mask coordinate are irrelevant, so above formula can be write as:

Wherein,

Mean convolution, For the vector matrix of N * N, each element is 3 * 1 vector (v _x', v _y', v _z') ^TE ^Wafer(x _s, y _s) three components in global coordinate system are

Wherein,

P=x, y, z, wherein V _p' be the scalar matrix of N * N, by the p component of each element of vector matrix V ', formed.Pointolite (x _s, y _s) aerial image on corresponding wafer position is

Wherein,

Expression is to the matrix delivery and ask square.H wherein _pBe (x with B _s, y _s) function, be designated as respectively With

, so above formula can be designated as:

Above formula obtains is that aerial image corresponding under spot light distributes, in step 205 under the partial coherence light illumination corresponding aerial image can be expressed as

Wherein $J_{\mathrm{sum}}=\underset{x_s}{\mathrm{\Σ}}\underset{y_s}{\mathrm{\Σ}}J(x_s,y_s).$

Step 206, the photoresist approximate model provided based on pertinent literature (Trans.Image Process., 2007,16:774～788), by adopting the sigmoid approximation to function, the photoresist effect is described:

$\mathrm{sigmoid}\left(I\right)=\frac{1}{1+\exp [-a(I-t_r)]}$

Wherein, a means the slope of photoresist approximate model, t _rThe threshold value that means the photoresist approximate model;

Calculate being imaged as in light source figure and photoresist corresponding to mask graph according to aerial image I:

$Z=\frac{1}{1+\exp [-a(I-t_r)]}---\left(12\right)$

Step 104, calculating target function D are for matrix of variables Ω _SGradient matrix

Pixel value sum J by each pixel on the light source figure _sumBe approximately given constant, obtain gradient matrix

Approximate value $\▿\tilde{D}\left({\mathrm{\Ω}}_S\right).$

Gradient matrix

For objective function D to matrix of variables Ω _SIn each element asked partial derivative to obtain; Although J _sumJ (x _s, y _s) function, but the present invention is approximately constant by it.This being similar to can be reduced gradient matrix

Computation complexity.On the other hand, emulation shows that this approximate can make the SESMO optimizing process more stable.Gradient matrix

In being calculated as of can being similar to of each element:

Wherein, 1 _{N * 1}Complete 1 vector for N * 1.

The present invention can adopt following two kinds of algorithm speed technologies, improves SESMO and optimizes speed, reduces the complexity of optimizing.First method is electric field intensity caching technology (electric field caching technique is called for short EFCT).From (13) formula, for the calculating target function gradient matrix

At first we need to calculate And Z.And, in order to calculate Z, we also need at first to calculate

Therefore calculating

Process in, we are only right

Once calculate, and its result of calculation reused, thus calculate Z and

Value.Second method is Fast Fourier Transform (FFT) (fast Fourier transform is called for short FFT) technology.Because (13) formula is known, each calculating

The time, we all need to calculate

.From (10) formula,

Computation process in include convolution algorithm.Utilize the FFT computing to replace convolution algorithm, we can be deformed into (10) formula:

p＝x，y，z。

Wherein, V _p' be (x _s, y _s) function, therefore it is designated as

Utilize steepest prompt drop method to upgrade matrix of variables Ω _S, upgrade Ω _SFor

For predefined light source Optimal Step Size.Further obtain corresponding current Ω _SLight source figure J, In the SESMO optimizing process, J (x _s, y _s) span be J (x _s, y _s) ∈ [0,1], Ω _S(x _s, y _s) span be Ω _S(x _s, y _s) ∈ [∞ ,+∞].

Step 105, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or upgrades matrix of variables Ω _SNumber of times reach predetermined upper limit value K _SThe time, enter step 106, otherwise return to step 104.

Step 106, calculating target function D are for matrix of variables Ω _MGradient matrix

Gradient matrix For objective function D to matrix of variables Ω _MIn each element carry out the differentiate acquisition.

In the present invention, gradient matrix

Can be calculated as:

Wherein, ^*Mean to get conjugate operation; ° expression is by matrix equal Rotate 180 degree on horizontal and vertical.

The present invention can adopt following two kinds of algorithm speed technologies, improves SESMO and optimizes speed, reduces the complexity of optimizing.First method is electric field intensity caching technology (electric field caching technique is called for short EFCT).From (14) formula, for the calculating target function gradient matrix At first we need to calculate

And Z.And, in order to calculate Z, we also need at first to calculate

Therefore calculating

Process in, we are only right Once calculate, and its result of calculation reused, thus calculate Z and

Value.Second method is Fast Fourier Transform (FFT) (fast Fourier transform is called for short FFT) technology.Because (14) formula has comprised a large amount of convolution algorithms, therefore calculate

Process there is higher complexity.In order to reduce computation complexity, we replace convolution algorithm with the FFT computing, thereby (14) formula is deformed into:

Wherein, C is the scalar matrix of a N * N, and each element is:

$C(m,n)=\exp \left[j2\mathrm{\π}(\frac{m}{N}+\frac{n}{N})\right]$ m，n＝1，2，...，N

In addition, each calculating

The time, we all need to calculate

From (10) formula, Computation process also include convolution algorithm.Utilize the FFT computing to replace convolution algorithm, we can be deformed into (10) formula:

p＝x，y，z。

Utilize steepest prompt drop method to upgrade matrix of variables Ω _M, upgrade Ω _MFor

For predefined photomask optimization step-length.Further obtain corresponding current Ω _MMask graph M,

In the SESMO optimizing process, the span of M (x, y) is M (x, y) ∈ [0,1], Ω _MThe span of (x, y) is Ω _M(x, y) ∈ [∞ ,+∞].Upgrade the two-value mask graph M of corresponding current M _b,

T generally _m=0.5.

Step 107, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or upgrades matrix of variables Ω _MNumber of times reach predetermined upper limit value K _MThe time, enter step 108, otherwise return to step 106.

Step 108, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or alternately upgrades matrix of variables Ω _SAnd Ω _MNumber of times reach predetermined upper limit value K _S-MThe time, enter step 109, otherwise return to step 104.

Step 109, stop optimizing, and by current light source figure J and two-value mask graph M _bBe defined as light source figure and mask graph after optimizing.

Embodiment of the present invention:

Be illustrated in figure 3 the schematic diagram of imaging in primary light source, initial mask and corresponding photoresist thereof.301 is the primary light source figure, and white represents luminous component, and black represents not luminous component.302 is the initial mask figure, is also targeted graphical simultaneously, and white represents opening portion, and black represents light-blocking part, and its critical size is 45nm.303 for adopt 301 as light source, 302 as after mask, imaging in the photoresist of etching system, image error is 2286 (image error is defined as the value of objective function here).

Be illustrated in figure 4 the schematic diagram of imaging in the independent optimum results of light source based on Abbe vector imaging model, initial mask figure and corresponding photoresist thereof.401 is the independent optimum results of light source based on Abbe vector imaging model.402 is the initial mask figure.403 for adopt 401 as light source, 402 as after mask, imaging in the photoresist of etching system, image error is 1234.

Be illustrated in figure 5 the schematic diagram of imaging in primary light source figure, the independent optimum results of mask based on Abbe vector imaging model and corresponding photoresist thereof.501 is the primary light source figure.502 is the independent optimum results of mask based on Abbe vector imaging model.503 for adopt 501 as light source, 502 as after mask, imaging in the photoresist of etching system, image error is 592.

Be illustrated in figure 6 the schematic diagram of imaging in light source figure after the SISMO method adopted based on Abbe vector imaging model is optimized, mask graph and corresponding photoresist thereof.601 is the light source figure after the SISMO method optimization adopted based on Abbe vector imaging model.602 is the mask graph after the SISMO method optimization adopted based on Abbe vector imaging model.603 for adopt 601 as light source, 602 as after mask, imaging in the photoresist of etching system, image error is 534.

Be illustrated in figure 7 the schematic diagram of imaging in light source figure after the SESMO method adopted based on Abbe vector imaging model is optimized, mask graph and corresponding photoresist thereof.701 is the light source figure after the SESMO method optimization adopted based on Abbe vector imaging model.702 is the mask graph after the SESMO method optimization adopted based on Abbe vector imaging model.703 for adopt 701 as light source, 702 as after mask, imaging in the photoresist of etching system, image error is 528.

Comparison diagram 3,4,5,6,7 is known, and with respect to primary light source and mask graph, the independent optimization method of light source and the independent optimization method of mask based on Abbe vector imaging model all can reduce image error, thereby improves the resolution of etching system.And optimize separately with respect to the independent optimization of light source and mask, the SISMO method based on Abbe vector imaging model and SESMO method have been introduced the light source variable in the photomask optimization process, have increased the optimization degree of freedom.Therefore the SISMO method based on Abbe vector imaging model and SESMO method can more efficiently reduction image errors, thus the resolution of more efficiently raising etching system.On the other hand, than the SISMO method, the SESMO method the present invention relates to can be by alternately optimizing light source and mask, effectively reduce the probability that optimized algorithm is absorbed in local optimum, thereby can access the optimum results that more approaches global optimum, and the resolution of more efficiently raising etching system.

Although combine accompanying drawing, the specific embodiment of the present invention has been described; but to those skilled in the art; under the premise without departing from the principles of the invention, can also make some distortion, replacement and improvement, these also should be considered as belonging to protection scope of the present invention.

Claims (2)

1. light source-the mask based on Abbe vector imaging model replaces optimization method, it is characterized in that, concrete steps are:

Step 101, light source is initialized as to size for N _S* N _SLight source figure J, it is the targeted graphical of N * N that mask graph M is initialized as to size N wherein _SWith N be integer;

Step 102, the pixel value that the upper light-emitting zone of primary light source figure J is set are 1, and the pixel value of light-emitting zone is not 0; Set N _S* N _SMatrix of variables Ω _S: as J (x _s, y _s)=1 o'clock,

As J (x _s, y _s)=0 o'clock, J (x wherein _s, y _s) mean each pixel (x on the light source figure _s, y _s) pixel value; The transmissivity that initial mask figure M upper shed part is set is 1, and the transmissivity in resistance light zone is 0; Set the matrix of variables Ω of N * N _M: when M (x, y)=1,

When M (x, y)=0, Wherein M (x, y) means the transmissivity of each pixel (x, y) on mask graph; Make two-value mask graph M _bInitial value be M;

Step 103, by objective function D be configured to the Euler's distance between imaging in photoresist that targeted graphical is corresponding with current light source figure and mask graph square,

Wherein For the pixel value of each pixel of targeted graphical, Z (x, y) means to utilize Abbe vector imaging model to calculate the pixel value of each pixel of imaging in current light source figure and photoresist corresponding to mask graph;

The concrete steps that the described Abbe of utilization vector imaging model calculates imaging in current light source and photoresist corresponding to mask are:

Step 201, mask graph M grid is turned to N * N sub regions;

Step 202, light source figure J grid is turned to N _S* N _SSub regions;

Step 203, for a single point light source (x _s, y _s), the aerial image I (x while obtaining this spot light on corresponding wafer position _s, y _s);

Step 204, judge whether to calculate the aerial image on the corresponding wafer positions of all pointolites, if enter step 205, otherwise return to step 203;

Step 205, according to Abbe Abbe method, to the aerial image I (x on the corresponding wafer position of each pointolite _s, y _s) superposeed, while obtaining the partial coherence light illumination, the aerial image I on wafer position;

Step 206, based on the photoresist approximate model, calculate the imaging in light source figure and photoresist corresponding to mask graph according to aerial image I;

Step 104, calculating target function D are for matrix of variables Ω _SGradient matrix Pixel value sum J by each pixel on the light source figure _sumBe approximately given constant, obtain gradient matrix

Approximate value

Utilize steepest prompt drop method to upgrade matrix of variables Ω _S, upgrade Ω _SFor

Wherein

For predefined light source Optimal Step Size, obtain corresponding current Ω _SLight source figure J, $J(x_s,y_s)=\frac{1}{2}[1+\cos {\mathrm{\Ω}}_S(x_s,y_s)];$

Step 105, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or upgrades matrix of variables Ω _SNumber of times reach predetermined upper limit value K _SThe time, enter step 106, otherwise return to step 104;

Step 106, calculating target function D are for matrix of variables Ω _MGradient matrix

Utilize steepest prompt drop method to upgrade matrix of variables Ω _M, upgrade Ω _MFor

Wherein

For predefined photomask optimization step-length, obtain corresponding current Ω _MMask graph M,

Upgrade the two-value mask graph M of corresponding current M _b,

t _mFor preset parameter;

Step 107, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or upgrades matrix of variables Ω _MNumber of times reach predetermined upper limit value K _MThe time, enter step 108, otherwise return to step 106;

Step 108, calculating current light source figure J and two-value mask graph M _bThe value of corresponding objective function D; When this value is less than predetermined threshold or New Alternate matrix of variables Ω more _SAnd Ω _MNumber of times reach predetermined upper limit value K _S-MThe time, enter step 109, otherwise return to step 104;

Step 109, stop optimizing, and by current light source figure J and two-value mask graph M _bBe defined as light source figure and mask graph after optimizing.

2. according to claim 1, the light source-mask based on Abbe vector imaging model replaces optimization method, it is characterized in that, in described step 203 for a single point light source (x _s, y _s) aerial image I (x while obtaining this spot light on corresponding wafer position _s, y _s) detailed process be:

The direction of setting optical axis is the z axle, and sets up global coordinate system according to the left-handed coordinate system principle; (α, beta, gamma) is the coordinate system after global coordinate system on mask (x, y, z) carries out Fourier transform, (α ', β ', γ ') be global coordinate system (x on wafer _w, y _w, z _w) carry out the coordinate system after Fourier transform;

Step 301, for a single point light source (x _s, y _s), the near field distribution E of the light wave that the calculation level light source sends N * N sub regions on mask; Wherein, the vector matrix that E is N * N, its each element is one 3 * 1 vector, means 3 components of the diffraction near field distribution of mask in global coordinate system;

Step 302, according near field distribution E, obtain the Electric Field Distribution of light wave at optical projection system entrance pupil rear Wherein,

For the vector matrix of N * N, its each element is one 3 * 1 vector, means 3 components of the Electric Field Distribution at entrance pupil rear in global coordinate system;

Step 303, to establish light wave direction of propagation in optical projection system approximate parallel with optical axis, further according to the Electric Field Distribution at entrance pupil rear

Obtain the Electric Field Distribution in optical projection system emergent pupil the place ahead

Wherein, the Electric Field Distribution in emergent pupil the place ahead

For the vector matrix of N * N, its each element is one 3 * 1 vector, means 3 components of the Electric Field Distribution in emergent pupil the place ahead in global coordinate system;

Step 304, according to the Electric Field Distribution in optical projection system emergent pupil the place ahead Obtain the Electric Field Distribution at optical projection system emergent pupil rear

Step 305, utilize Wolf Wolf optical imagery theory, according to the Electric Field Distribution at emergent pupil rear

Obtain the Electric Field Distribution E on wafer ^Wafer, and according to E ^WaferAerial image I (x on the corresponding wafer position of acquisition point light source _s, y _s).

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