CN102323722A - Method for acquiring mask space image based on Abbe vector imaging model - Google Patents

Abstract

The present invention provides a method for acquiring a mask space image based on an Abbe vector imaging model. Concrete steps of the method comprise: rasterizing a mask pattern M into N*N subregions; rasterizing a light source surface into a plurality of point light sources according to the shapes of partial coherent light sources, wherein the coordinate (xs, ys) of a center point of each raster region represents the coordinate of the point light source corresponding to the raster region; calculating the mask space image I (alphas, betas) on a image surface corresponding to each point light source; overlaying the mask space images I (alphas, betas) of each point light source according to the Abbe method to acquire the mask space image I on the image surface positions corresponding to the partial coherent light sources. According to the present invention, the light source surface can be rasterized into a plurality of the point light sources; the mask space image calculated according to each point light source has high precision; the method can be applicable for the light sources with different surface shapes.

Description

Obtain the method for mask aerial image based on Abbe vector imaging model

Technical field

The present invention relates to a kind ofly obtain the method for mask aerial image, belong to photoetching resolution enhancement techniques field based on Abbe (Abbe) vector imaging model.

Background technology

Current large scale integrated circuit generally adopts etching system manufacturing.Etching system mainly is divided into: four parts such as illuminator (comprising light source and condenser), mask, optical projection system and wafer.The light that light source sends is incident to mask, the opening portion printing opacity of mask after focusing on through condenser; Through behind the mask, light is incident on the wafer that scribbles photoresist via optical projection system, so just mask pattern is replicated on the wafer.

The etching system of main flow is the ArF degree of depth ultraviolet photolithographic system of 193nm at present; Along with the photoetching technique node gets into 45nm-22nm; The critical size of circuit has been far smaller than the wavelength of light source, so interference of light and diffraction phenomena are more remarkable, causes optical patterning to produce distortion and fuzzy.Etching system must adopt RET for this reason, in order to improve image quality.Phase-shift mask (phase-shifting mask PSM) and optical proximity correction (optical proximity correction OPC) are important photoetching resolution enhancement techniques.PSM adopts light transmission medium and resistance light medium to process, and the light transmission part is equivalent to opening to light.PSM is through change the topological structure and the etch depth of mask light transmission part (being opening) in advance, and the amplitude and the phase place of the electric field intensity of modulation mask exit facet are to reach the purpose that improves imaging resolution.The method of OPC through changing mask pattern and on mask, adding tiny auxiliary pattern reaches the purpose that improves optical patterning resolution.

In order further to improve the etching system imaging resolution, industry generally adopts immersion lithographic system at present.Immersion lithographic system enlarges numerical aperture (numerical aperture NA) between the lower surface of last lens of projection objective and photoresist, having added refractive index greater than 1 light transmission medium thereby reach, and improves the purpose of imaging resolution.Because immersion lithographic system has high NA (NA＞1) characteristic; And when NA＞0.6; The vector imaging characteristic of electromagnetic field can not be ignored the influence of the aerial image on the wafer position, and is therefore no longer suitable for its scalar imaging model of immersion lithographic system.In order to obtain the imaging characteristic of accurate immersion lithographic system, must adopt the vector imaging model that the mask in the immersion lithographic system is optimized.

In the patented claim of " a kind of phase-shift mask optimization method " that the applicant proposes on the same day based on Abbe vector imaging model, disclose a kind of employing vector model phase-shift mask has been optimized, make it can be adapted to the immersion lithographic system of high NA.Its basic thought is: the phase place of adjacent apertures in the three-dimensional phase-shift mask and central regional transmission is set, makes it have 180 ° phase differential; Matrix of variables Ω is set, Euler's distance of the difference that objective function D is configured to form images in the targeted graphical photoresist corresponding with current mask square; Utilize the optimization of matrix of variables Ω and objective function D guiding phase-shift mask.In said method, obtaining forms images in the photoresist is the committed step of realization to phase-shift mask optimization; And the calculating that forms images in the corresponding photoresist of mask is based on that aerial image on the corresponding wafer position calculates, thereby the calculating of mask aerial image is played crucial effects in the optimizing process of mask.

Prior art (Proc.if SPIE 2003.5040:78-91.) is to the partial coherence imaging system, proposed a kind of method of the calculating mask aerial image based on Hopkins (Thelma Hopkins) formula.It does not consider the response difference of optical projection system to difference light source incident ray on the surface of light source.But owing to the incident angle of diverse location light on the surface of light source is different, its effect to optical projection system there are differences, and forms images and the bigger deviation of physical presence in the air that therefore adopts existing method to obtain, and then influences the optimization effect of mask.

Prior art (Proc.of SPIE 2010.7640:76402Y1-76402Y9.) has proposed a kind of method of computer memory picture to the partial coherence imaging system of utilizing the partial coherence light source.It does not provide the analytical expression of the matrix form of aerial image under the vector imaging model, and the sequencing that therefore is not suitable for lithography model is handled, and the research of high NA etching system intermediate-resolution enhancement techniques optimization method.

Summary of the invention

The purpose of this invention is to provide a kind of method of obtaining the mask aerial image based on Abbe vector imaging model.This method is carried out rasterizing to the partial coherence light source face of etching system, obtains aerial image to each grid region central point light source coordinate, and based on the Abbe method, the aerial image I (α corresponding to each pointolite _s, β _s) superpose, obtain aerial image according to this method and have higher accuracy.

Realize that technical scheme of the present invention is following:

A kind ofly obtain the method for mask aerial image based on Abbe vector imaging model, concrete steps are:

Step 101, mask pattern M grid is turned to N * N sub regions;

Step 102, according to the shape of partial coherence light source surface of light source is tiled into a plurality of pointolites, with each grid region center point coordinate (x _s, y _s) represent the pairing pointolite coordinate of this grid region;

Step 103, to a single point light source, utilize its coordinate (x _s, y _s) aerial image I (α when obtaining this spot light on the corresponding wafer position _s, β _s);

Step 104, judge whether to calculate the aerial image on the corresponding wafer positions of all pointolites, if then get into step 105, otherwise return step 103;

Step 105, according to Abbe Abbe method, the aerial image I (α corresponding to each pointolite _s, β _s) superpose, when obtaining the partial coherence light illumination, the aerial image I on the wafer position.

The detailed process of step 103 according to the invention is:

The setting global coordinate system is: the direction with optical axis is the z axle, and according to the left-handed coordinate system principle with the z axle set up global coordinate system (x, y, z).

Step 201, according to pointolite coordinate (x _s, y _s), the light wave that the calculation level light source sends is through the near field distribution E of N * N sub regions on the mask; Wherein, E is the vector matrix of N * N, and its each element is one 3 * 1 vector, 3 components of the diffraction near field distribution of mask in the expression global coordinate system;

Step 202, obtain light wave wherein in the Electric Field Distribution

at optical projection system entrance pupil rear according near field distribution E;

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

Step 203, to establish light wave direction of propagation in optical projection system approximate parallel with optical axis; Further obtain light wave wherein in the Electric Field Distribution

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

at entrance pupil rear; The Electric Field Distribution in emergent pupil the place ahead

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

Step 204, according to the projection system in front of the exit pupil of the electric field distribution

Get behind the exit pupil of the projection system of the electric field distribution

Step 205, utilize Wolf Wolf optical imagery theoretical, according to the Electric Field Distribution at emergent pupil rear

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

Beneficial effect

The present invention is tiled into a plurality of pointolites with surface of light source; Calculate respectively in its corresponding air to the difference light source and to form images; Have the high advantage of degree of accuracy, this method is applicable to difform light source, and satisfies the lithography simulation demand of 45nm and following technology node.

Secondly, the present invention has set up the analytical expression of the matrix form of aerial image under the vector imaging model, and favourable sequencing with the optical patterning model is handled, and the research of high NA etching system intermediate-resolution enhancement techniques optimization method.

Description of drawings

Fig. 1 sends the synoptic diagram that light wave forms images for pointolite on wafer position after mask, optical projection system.

Fig. 2 is the process flow diagram of computer memory of the present invention as method.

Fig. 3 is for carrying out the synoptic diagram of rasterizing in the embodiment of the invention to circular portion coherent source face.

The impulse Response Function contrast synoptic diagram that Fig. 4 emits beam for different pointolites for the lithographic projection system.

Fig. 5 is for adopting the aerial image contrast synoptic diagram that obtains after the different light source rasterizing density.

Embodiment

Further the present invention is elaborated below in conjunction with accompanying drawing.

Variable predefine

As shown in Figure 1, the direction of setting optical axis is the z axle, and according to the left-handed coordinate system principle with the z axle set up global coordinate system (x, y, z).If the world coordinates of any point light source is (x on the partial coherence light source face _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), then the relation between world coordinates and the direction cosine is:

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

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

If the world coordinates of any point is on the mask (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), wherein (α; Beta, gamma) be that mask (object plane) is gone up global coordinate system (x, y z) are carried out coordinate system after the Fourier transform.

If it is (x that wafer (image planes) is gone up the world coordinates of any point _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 that wafer (image planes) is gone up global coordinate system (x _w, y _w, z _w) carry out the coordinate system after the Fourier transform.

Transformational relation between global coordinate system and the local coordinate system:

Set up local coordinate system (e _⊥, e _P), e _⊥Axle for light source emit beam in the direction of vibration of TE polarized light, the eP axle is the emit beam direction of vibration of middle TM polarized light of light source.The plane that wave vector is made up of wave vector and optical axis for

is called the plane of incidence; 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.Then the transformational relation of global coordinate system and local coordinate system is:

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

Wherein, E _x, E _yAnd E _zBe respectively that light source sends the component of light wave electric field in global coordinate system, E _⊥And E _PBe 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, $\mathrm{\ρ}=\sqrt{{\mathrm{\α}}^2+{\mathrm{\β}}^2}.$

As shown in Figure 2, the concrete steps of obtaining the method for aerial image are:

Step 101, mask pattern M grid is turned to N * N sub regions.

Step 102, according to the shape of partial coherence light source surface of light source is tiled into a plurality of zones, each zone is approximate with pointolite.Each grid region center point coordinate (x _s, y _s) represent the pairing pointolite coordinate of this grid region.

Because there is multiple shape in the surface of light source of employed partial coherence light source in the etching system, therefore can carry out rasterizing to it according to the shape of surface of light source.As shown in Figure 3; For example when the partial coherence light source was circle, said shape according to the partial coherence light source is carried out grid with surface of light source and turned to: with central point on the surface of light source was the center of circle, and k the concentric circless different with the radius of setting in advance are divided into k zone with the sphere shape light face; Said k zone begun to carry out from inside to outside 1～k numbering from the center circle district; 301 is the center circle district among the figure, and 302 is the 3rd zone, and 303 is k zone of outermost.With each area dividing that is numbered 2～k is a plurality of fan-shaped grid region.Each area dividing that the present invention preferably will be numbered 2～k becomes the fan-shaped grid region of same number.

Step 103, to a single point light source, utilize its coordinate (x _s, y _s) aerial image I (α when obtaining this spot light on the corresponding wafer position _s, β _s).

Step 104, judge whether to calculate the aerial image on the corresponding wafer positions of all pointolites, if then get into step 105, otherwise return step 103.

Step 105, according to the Abbe method, the aerial image I (α corresponding to each pointolite _s, β _s) superpose, when obtaining the partial coherence light illumination, the aerial image I on the wafer position.

In the face of step 103 is directed against a single point light source, utilize its coordinate (x down _s, y _s) when obtaining this spot light on the corresponding wafer position process of aerial image be further elaborated:

Step 201, according to pointolite coordinate (x _s, y _s), the light wave that the calculation level light source sends is through the near field distribution E of N * N sub regions on the mask.

Wherein, E is that the vector matrix of N * N is (if all elements of a matrix is matrix or vector; Then be called vector matrix), each element in this vector matrix is one 3 * 1 vector, 3 components of the diffraction near field distribution of mask in the expression global coordinate system.E representes that two matrix corresponding elements multiply each other.

is the vector matrix of one N * N, and each element is the electric field intensity of electric field in global coordinate system that pointolite sends light wave; As establish the electric field that a pointolite on the partial coherence light source sends light wave and in local coordinate system, be expressed as

Then this electric field is expressed as in global coordinate system:

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

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

$=\exp \left(\frac{j2\mathrm{\π}{\mathrm{\β}}_{s}m\·\mathrm{pixel}}{\mathrm{\λ}}\right)\exp \left(\frac{j2{\mathrm{\π\α}}_{s}n\·\mathrm{pixel}}{\mathrm{\λ}}\right),$ m，n＝1，2，...，N

Wherein, pixel representes the length of side of all subregion on the mask pattern.

Step 202, 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 the mask can be regarded a secondary sub-light source as, the center of the subregion coordinate as this subregion is theoretical according to Fourier optics, can the Electric Field Distribution in optical projection system entrance pupil the place ahead be expressed as 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 have N * N sub regions on the mask; Therefore the Electric Field Distribution

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

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

Because the reduction magnification of optical projection system is bigger; Be generally 4 times; This moment, the numerical aperture of object space was less; Cause the axial component of entrance pupil the place ahead Electric Field Distribution

to ignore, so optical projection system entrance pupil the place ahead is identical with the Electric Field Distribution at entrance pupil rear, promptly

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

Wherein, Owing to have N * N sub regions on the mask; Therefore the Electric Field Distribution

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

Step 203, to establish light wave direction of propagation in optical projection system approximate parallel with optical axis, further obtains the Electric Field Distribution

of light wave in optical projection system emergent pupil the place ahead according to the Electric Field Distribution

at entrance pupil rear

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:

$E_l^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′})=\mathrm{cUe}{E}_b^{\mathrm{ent}}(\mathrm{\α},\mathrm{\β})---\left(4\right)$

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

is the vector matrix of N * N; Each element in this vector matrix is one 3 * 1 vector, 3 components of the Electric Field Distribution in emergent pupil the place ahead in the expression global coordinate system; C is the constant correction factor, and low-pass filter function U is the scalar matrix of N * N, and the numerical aperture of expression optical projection system is 1 in the inner value of pupil promptly to the limited receiving ability of diffraction spectrum, and the outside value of pupil is 0, the concrete expression 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 the 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 _wBe the refractive index of etching system picture side immersion liquid, R is the reduction magnification of preferred view system, is generally 4.

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

$E_l^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′})=\frac{1}{{\mathrm{\λr}}^{\′}}\sqrt{{\mathrm{\γ}}^{\′}\mathrm{\γ}}\frac{n_w}{R}\mathrm{U\; e\; F}\left\{E\right\}---\left(5\right)$

Step 204, according to the projection system in front of the exit pupil of the electric field distribution

Get behind the exit pupil of the projection system of the electric field distribution

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

and

and

is following:

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

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

Wherein, m, n=1,2 ..., N, α '=cos φ ' sin θ ', β '=sin φ ' sin θ ', γ '=cos θ ', promptly the optical projection system emergent pupil direction cosine (wave vector) that are incident to the plane wave of image planes are k '=(α ', β ', γ '); φ ' and θ ' are respectively the position angle and the elevations angle of wave vector, and then the relational expression of

and

is:

$E_b^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′})=\mathrm{Ve}{E}_l^{\mathrm{ext}}({\mathrm{\α}}^{\′},{\mathrm{\β}}^{\′})---\left(6\right)$

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

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

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

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

Step 205, utilize the optical imagery of Wolf theoretical, according to the Electric Field Distribution at emergent pupil rear

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

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

Wherein,

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

$E^{\mathrm{wafer}}=\frac{2\mathrm{\π}}{n_{w}R}{F}^{-1}\left\{\sqrt{\frac{\mathrm{\γ}}{{\mathrm{\γ}}^{\′}}}\mathrm{Ve\; Ue\; F}\right\{E\left\}\right\}---\left(8\right)$

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

$E^{\mathrm{wafer}}({\mathrm{\α}}_s,{\mathrm{\β}}_s)=\frac{2\mathrm{\π}}{n_{w}R}{F}^{-1}\left\{\sqrt{\frac{\mathrm{\γ}}{{\mathrm{\γ}}^{\′}}}\mathrm{Ve\; Ue\; F}\right\{{E_i}^{\′}\mathrm{eBeM}\left\}\right\}---\left(9\right)$

Because E _i' middle element value and mask coordinate are irrelevant, so following formula can be write as:

$E^{\mathrm{wafer}}({\mathrm{\α}}_s,{\mathrm{\β}}_s)=\frac{2\mathrm{\π}}{n_{w}R}{F}^{-1}\left\{V^{\′}\right\}\⊗\left(\mathrm{Be\; M}\right)$

Wherein,

The expression convolution,

Be the vector matrix of N * N, each element is 3 * 1 vector (v _x', v _y', v _z') ^T

E then ^Wafer(α _s, β _s) three components in global coordinate system do

$E_P^{\mathrm{wafer}}({\mathrm{\α}}_s,{\mathrm{\β}}_s)=H_p\⊗\left(\mathrm{Be\; M}\right)$

Wherein,

P=x, y, z, wherein V _p' be the scalar matrix of N * N, form by the x component of each element of vector matrix V '

$I({\mathrm{\α}}_s,{\mathrm{\β}}_s)=\underset{p=x,y,z}{\mathrm{\Σ}}{\left|\right|H_p\⊗\left(\mathrm{Be\; M}\right)\left|\right|}_2^2$

Wherein

expression is to the matrix delivery and ask square.H wherein _pBe (α with B _s, β _s) function, be designated as respectively

With

Therefore following formula can be designated as:

$I({\mathrm{\α}}_s,{\mathrm{\β}}_s)=\underset{p=x,y,z}{\mathrm{\Σ}}{\left|\right|H_p^{{\mathrm{\α}}_s{\mathrm{\β}}_s}\⊗\left(B^{{\mathrm{\α}}_s{\mathrm{\β}}_s}\mathrm{e\; M}\right)\left|\right|}_2^2$

Following formula obtains is that the aerial image that mask is corresponding under the spot light distributes, then in the step 105 under the partial coherence light illumination mask aerial image can be expressed as

$I=\frac{1}{N_s}\underset{{\mathrm{\α}}_s}{\mathrm{\Σ}}\underset{{\mathrm{\β}}_s}{\mathrm{\Σ}}\underset{p=x,y,z}{\mathrm{\Σ}}{\left|\right|H_p^{{\mathrm{\α}}_s{\mathrm{\β}}_s}\⊗\left(B^{{\mathrm{\α}}_s{\mathrm{\β}}_s}\mathrm{e\; M}\right)\left|\right|}_2^2$

Wherein, N _sIt is the sampling number of partial coherence light source.

Embodiment of the present invention:

As shown in Figure 4,401 two pointolite A and B on surface of light source, being got.The x component of the 402 impulse Response Function H that emit beam for different pointolites for photoetching optical projection system on the y=0 position on the pupil.The y component of the 403 impulse Response Function H that emit beam for different pointolites for photoetching optical projection system on the y=0 position on the pupil.The z component of the 404 impulse Response Function H that emit beam for different pointolites for photoetching optical projection system on the y=0 position on the pupil.

As shown in Figure 5,501 is initial two-value mask synoptic diagram, and its critical size is 45nm, and it is 1 that white is represented its transmissivity of transmission region, black representative resistance light zone, and its transmissivity is 0.Mask pattern is positioned at the xy plane, and lines are parallel with the y axle.502 for turning to the surface of light source grid behind 31 * 31 pointolites binary mask aerial image result under the resulting ring illumination.503 for turning to the surface of light source grid behind 2 * 2 pointolites binary mask aerial image result under the resulting ring illumination.504 two kinds of Y=0 place curve of light distribution contrasts that method obtains.505 for the surface of light source grid is turned to behind 31 * 31 pointolites after the curve of light distribution that obtains.506 for turning to the surface of light source grid the resulting curve of light distribution behind 2 * 2 pointolites.

402,403 and 404 can find from Fig. 4, for different pointolites, exist than big-difference between the impulse Response Function of lithographic projection system.This moment is if all adopt identical impulse Response Function bring error will inevitably for obtaining of aerial image to different electric light sources.505 and 506 can find in the comparison diagram 5, and to the rasterizing of surface of light source employing different densities, light distribution has than big-difference.Above the result proved that the suitable method of under super large NA optical patterning employing carries out importance and the meaning that the present invention possessed of the aerial image of rasterizing and pointwise calculating mask to the partial coherence light source.

Though described embodiment of the present invention in conjunction with accompanying drawing, for the technician in present technique field,, can also do some distortion, replacement and improvement not breaking away under the prerequisite of the present invention, these also are regarded as belonging to protection scope of the present invention.

Claims (4)

1. one kind is obtained the method for mask aerial image based on Abbe vector imaging model, it is characterized in that concrete steps are:

Step 101, mask pattern M grid is turned to N * N sub regions;

Step 102, according to the shape of partial coherence light source surface of light source is tiled into a plurality of pointolites, with each grid region center point coordinate (x _s, y _s) represent the pairing pointolite coordinate of this grid region;

Step 103, to a single point light source, utilize its coordinate (x _s, y _s) aerial image I (α when obtaining this spot light on the corresponding wafer position _s, β _s);

Step 104, judge whether to calculate the aerial image on the corresponding wafer positions of all pointolites, if then get into step 105, otherwise return step 103;

Step 105, according to Abbe Abbe method, the aerial image I (α corresponding to each pointolite _s, β _s) superpose, when obtaining the partial coherence light illumination, the aerial image I on the wafer position.

2. obtain method for imaging in the mask air according to claim 1 is said; It is characterized in that; When described partial coherence light source is circle; Said shape according to the partial coherence light source turns to the surface of light source grid: with central point on the surface of light source is the center of circle; K the concentric circless different with the radius of setting in advance are divided into k+1 zone with sphere shape light face zoning, and said k+1 zone begun to carry out from inside to outside 1～k+1 numbering from the center circle district, are a plurality of fan-shaped grid region with each area dividing that is numbered 2～k.

3. obtain method for imaging in the mask air according to claim 2 is said, it is characterized in that, the number of the fan-shaped grid region that said each zone that is numbered 2～k is divided is identical.

4. obtain method for imaging in the mask air according to claim 1 is said, it is characterized in that the detailed process of said step 103 is:

The setting global coordinate system is: the direction with optical axis is the z axle, and according to the left-handed coordinate system principle with the z axle set up global coordinate system (x, y, z);

Step 201, according to pointolite coordinate (x _s, y _s), the light wave that the calculation level light source sends is through the near field distribution E of N * N sub regions on the mask; Wherein, E is the vector matrix of N * N, and its each element is one 3 * 1 vector, 3 components of the diffraction near field distribution of mask in the expression global coordinate system;

Step 202, obtain light wave wherein in the Electric Field Distribution

at optical projection system entrance pupil rear according near field distribution E;

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

Step 203, to establish light wave direction of propagation in optical projection system approximate parallel with optical axis; Further obtain light wave wherein in the Electric Field Distribution

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

at entrance pupil rear; The Electric Field Distribution in emergent pupil the place ahead is the vector matrix of N * N; Its each element is one 3 * 1 vector, 3 components of the Electric Field Distribution in emergent pupil the place ahead in the expression global coordinate system;

Step 204, the front exit pupil of the projection system according to the electric field distribution

Get behind the exit pupil of the projection system of the electric field distribution

Step 205, utilize Wolf Wolf optical imagery theoretical, according to the Electric Field Distribution at emergent pupil rear

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

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