CN102323722B - 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

Method for obtaining mask space image based on Abbe vector imaging model

Technical Field

The invention relates to a method for obtaining a mask space image based on an Abbe (Abbe) vector imaging model, belonging to the technical field of photoetching resolution enhancement.

Background

Current large scale integrated circuits are commonly manufactured using photolithographic systems. The lithography system is mainly divided into: the device comprises an illumination system (comprising a light source and a condenser), a mask, a projection system and a wafer. Light rays emitted by the light source are focused by the condenser lens and then are incident to the mask, and the opening part of the mask is transparent; after passing through the mask, light is incident on the photoresist-coated wafer via the projection system, thus replicating the mask pattern on the wafer.

The mainstream lithography system at present is an ArF deep ultraviolet lithography system of 193nm, and as the node of the lithography technology enters 45nm-22nm, the critical dimension of a circuit is far smaller than the wavelength of a light source, so that the interference and diffraction phenomena of light are more remarkable, and the lithography imaging is distorted and blurred. For this reason, the lithography system must employ resolution enhancement techniques to improve the imaging quality. Phase-shifting mask (PSM) and Optical Proximity Correction (OPC) are important lithographic resolution enhancement techniques. The PSM is made of a light-transmitting medium and a light-blocking medium, and the light-transmitting part is equivalent to an opening for light. The PSM modulates the amplitude and the phase of the electric field intensity of the emergent surface of the mask by changing the topological structure and the etching depth of the light-transmitting part (namely the opening) of the mask in advance so as to achieve the purpose of improving the imaging resolution. OPC achieves the purpose of improving the photoetching imaging resolution by changing the mask pattern and adding a fine auxiliary pattern on the mask.

In order to further improve the imaging resolution of the lithography system, an immersion lithography system is commonly used in the industry. The immersion lithography system adds a light-transmitting medium with the refractive index larger than 1 between the lower surface of the last lens of the projection objective and the photoresist, thereby achieving the purposes of enlarging the numerical aperture (numerical aperture NA) and improving the imaging resolution. Since the immersion lithography system has a high NA (NA > 1) characteristic, and when NA > 0.6, the influence of the vector imaging characteristic of the electromagnetic field on the aerial image at the wafer position cannot be ignored, the scalar imaging model for the immersion lithography system is no longer applicable. In order to obtain accurate imaging characteristics of an immersion lithography system, a mask in the immersion lithography system must be optimized using a vector imaging model.

In the patent application of "a phase shift mask optimization method based on an Abbe vector imaging model" proposed by the applicant on the same day, a method for optimizing a phase shift mask by using a vector model is disclosed, so that the method can be suitable for a high-NA immersion lithography system. The basic idea is as follows: setting phases of adjacent openings and a central transmission area in the three-dimensional phase shift mask to have a phase difference of 180 degrees; setting a variable matrix omega, and constructing a target function D as the square of the Euler distance of the difference between a target graph and an image in the photoresist corresponding to the current mask; the optimization of the phase shift mask is guided by the variable matrix omega and the objective function D. Obtaining the image in the photoresist in the method is a key step for realizing optimization of the phase shift mask, and the calculation of the image in the photoresist corresponding to the mask is calculated based on the aerial image on the corresponding wafer position, so that the calculation of the aerial image of the mask plays a crucial role in the optimization process of the mask.

The prior art (proc. if SPIE 2003.5040: 78-91.) proposes a method of calculating a mask aerial image based on the Hopkins (Hopkins) formula for a partially coherent imaging system. It does not take into account the difference in the response of the projection system to the incident light of different point sources on the light source plane. However, because the incident angles of the light rays at different positions on the light source surface are different, the effects of the light rays on the projection system are different, so that the imaging in the air obtained by the existing method has larger deviation from the actual imaging, and the optimization effect of the mask is further influenced.

The prior art (proc.of SPIE 2010.7640: 76402Y1-76402Y9.) proposes a method of calculating an aerial image for a partially coherent imaging system that utilizes a partially coherent light source. The method does not provide an analytical expression in a matrix form of the aerial image under the vector imaging model, so the method is not suitable for the programming processing of the photoetching model and the research of the resolution enhancement technology optimization method in the high-NA photoetching system.

Disclosure of Invention

The invention aims to provide a method for acquiring a mask space image based on an Abbe vector imaging model. The method is used for rasterizing a partial coherent light source surface of a photoetching system, acquiring a space image aiming at a central point light source coordinate of each grid area, and processing a space image I (alpha) corresponding to each point light source based on an Abbe method_s，β_s) And the space image obtained according to the method has higher accuracy.

The technical scheme for realizing the invention is as follows:

a method for obtaining a mask space image based on an Abbe vector imaging model comprises the following specific steps:

step 101, rasterizing a mask pattern M into N multiplied by N sub-regions;

step 102, gridding the light source surface into a plurality of point light sources according to the shape of the partial coherent light source, and using the central point coordinate (x) of each grid area_s，y_s) Representing the point light source coordinates corresponding to the grid area;

step 103, aiming at the single point light source, utilizing the coordinate (x) thereof_s，y_s) Obtaining a space image I (alpha) at the position corresponding to the wafer when the point light source is illuminated_s，β_s)；

Step 104, judging whether the space images of the positions of the wafer corresponding to all the point light sources are calculated, if so, entering step 105, otherwise, returning to step 103;

step 105, according to Abbe's method, corresponding space image I (alpha) to each point light source_s，β_s) And (4) performing superposition to obtain a space image I on the position of the wafer when the partially coherent light source is used for illumination.

The specific process of step 103 of the present invention is:

setting a global coordinate system as follows: and establishing a global coordinate system (x, y, z) by taking the direction of the optical axis as a z-axis and taking the z-axis as a principle of a left-hand coordinate system.

Step 201, according to the coordinates (x) of the point light source_s，y_s) Calculating the near-field distribution E of the light waves emitted by the point light source passing through the NxN sub-regions on the mask; wherein E is an N × N vector matrix, each element of which is a 3 × 1 vector representing 3 components of the diffracted near-field distribution of the mask in the global coordinate system;

step 202, obtaining the electric field distribution of the light wave behind the entrance pupil of the projection system according to the near field distribution E

Wherein,

a vector matrix of N × N, each element of which is a 3 × 1 vector, representing 3 components of the electric field distribution behind the entrance pupil in the global coordinate system;

step 203, setting the propagation direction of the light wave in the projection system to be approximately parallel to the optical axis, and further according to the electric field distribution behind the entrance pupil

Obtaining electric field distribution of light waves in front of exit pupil of projection systemWherein the electric field distribution in front of the exit pupil

A vector matrix of N × N, each element of which is a 3 × 1 vector, representing 3 components of the electric field distribution in front of the exit pupil in the global coordinate system;

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

Obtaining electric field distribution behind the exit pupil of a projection system

Step 205, using Walf Wolf optical imaging theory, according to the electric field distribution behind the exit pupil

Obtaining an electric field distribution E at a wafer location^waferAnd according to E^waferObtaining an aerial image I (alpha) of the point light source corresponding to the position of the wafer_s，α_s)。

Advantageous effects

The invention grids the light source surface into a plurality of point light sources, respectively calculates the corresponding in-air imaging aiming at different point light sources, has the advantage of high precision, can be suitable for light sources with different shapes, and meets the photoetching simulation requirements of technical nodes of 45nm and below.

Secondly, the invention establishes an analytical expression of the space image under the vector imaging model in a matrix form, and is beneficial to the programming processing of the photoetching imaging model and the research of the resolution enhancement technology optimization method in the high NA photoetching system.

Drawings

FIG. 1 is a schematic diagram of a light wave emitted from a point light source passing through a mask and a projection system to form an image at a wafer position.

FIG. 2 is a flow chart of a method of computing an aerial image according to the present invention.

FIG. 3 is a schematic diagram of rasterizing a circular partially coherent light source plane in an embodiment of the present invention.

FIG. 4 is a graph showing a comparison of the impulse response functions of the lithographic projection system for light from different point sources.

Fig. 5 is a schematic diagram of the spatial image contrast obtained after different light source rasterization densities are adopted.

Detailed Description

The present invention will be further described in detail with reference to the accompanying drawings.

Variable predefinition

As shown in fig. 1, the direction of the optical axis is set as the z-axis, and a global coordinate system (x, y, z) is established with the z-axis according to the principle of the left-hand coordinate system. Let the global coordinate of any point light source on the partially coherent light source surface be (x)_s，y_s，z_s) The cosine of the direction of the plane wave emitted from the point light source and incident on the mask is (alpha)_s，β_s，γ_s) Then the relationship between the global coordinate 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_mIs the projection system object-side numerical aperture.

Assuming that the global coordinate of any point on the mask is (x, y, z), the direction cosine of the plane wave incident from the mask to the projection system entrance pupil is (α, β, γ) based on the diffraction principle, where (α, β, γ) is the coordinate system after fourier transform of the global coordinate system (x, y, z) on the mask (object plane).

Let the global coordinate of any point on the wafer (image plane) be (x)_w，y_w，z_w) The direction cosine of the plane wave incident from the projection system exit pupil to the image plane is (α ', β', γ '), where (α', β ', γ') is the global coordinate system (x) on the wafer (image plane)_w，y_w，z_w) And (5) carrying out Fourier transform on the coordinate system.

Conversion relationship between global coordinate system and local coordinate system:

establishing a local coordinate system (e)_⊥，e_P)，e_⊥The axis is the vibration direction of the TE polarized light in the light emitted by the light source, and the eP axis is the vibration direction of the TM polarized light in the light emitted by the light source. Wave vector of

The plane formed by the wave vector and the optical axis is called the incident plane, the vibration direction of the TM polarized light is in the incident plane, and the vibration direction of the TE polarized light is perpendicular to the incident plane. The transformation relationship between the global coordinate system and the 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 is_x、E_yAnd E_zRespectively the component of the light wave electric field emitted by the light source in the global coordinate system, E_⊥And E_PThe component of the light wave electric field emitted by the light source in the local coordinate system is as follows:

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

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

as shown in fig. 2, the method for obtaining the aerial image includes the following specific steps:

step 101, the mask pattern M is rasterized into N × N sub-regions.

Step 102, the light source surface is rasterized into a plurality of areas according to the shape of the partial coherent light source, and each area is approximated by a point light source. Center point coordinate (x) of each grid region_s，y_s) And representing the point light source coordinates corresponding to the grid area.

Because the light source face of a partially coherent light source used in a lithography system has a variety of shapes, it can be rasterized according to the shape of the light source face. As shown in fig. 3, for example, when the partially coherent light source is circular, the light source surface is rasterized according to the shape of the partially coherent light source as follows: the circular light source surface is divided into k regions by taking a central point on the light source surface as a circle center and using k concentric circles with different preset radiuses, the k regions are numbered from the central circle region from inside to outside by 1-k, 301 in the figure is the central circle region, 302 is a 3 rd region, and 303 is a k-th region on the outermost side. Each region numbered 2-k is divided into a plurality of sector-shaped grid regions. In the present invention, each of the regions numbered 2 to k is preferably divided into the same number of sector-shaped grid regions.

Step 103, aiming at the single point light source, utilizing the coordinate (x) thereof_s，y_s) Obtaining a space image I (alpha) at the position corresponding to the wafer when the point light source is illuminated_s，β_s)。

And step 104, judging whether the space images of the positions of the wafer corresponding to all the point light sources are calculated, if so, entering step 105, otherwise, returning to step 103.

Step 105, according to the Abbe method, corresponding space image I (alpha) to each point light source_s，β_s) And (4) performing superposition to obtain a space image I on the position of the wafer when the partially coherent light source is used for illumination.

The following step 103 is directed to a single point light source, using its coordinates (x)_s，y_s) The process of obtaining the aerial image at the corresponding wafer position when the point light source is illuminated is further detailed:

step 201, according to the coordinates (x) of the point light source_s，y_s) And calculating the near-field distribution E of the light wave emitted by the point light source passing through the N multiplied by N sub-regions on the mask.

Where E is an N × N vector matrix (if all elements of a matrix are matrices or vectors, it is called a vector matrix), and each element in the vector matrix is a vector matrixIs a 3 x 1 vector representing the 3 components of the diffracted near-field distribution of the mask in the global coordinate system. e represents the multiplication of the corresponding elements of the two matrices.

Is an NxN vector matrix, and each element is an electric field vector of an electric field of the light wave emitted by the point light source in a global coordinate system; if the electric field of the light wave emitted by a point light source on the partially coherent light source is expressed as a local coordinate system

The electric field is then expressed in the global coordinate system as:

the diffraction matrix B of the mask is an N × N scalar matrix in which each element is a scalar, and according to the Hopkins (Hopkins) approximation, 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 represents the side length of each sub-area on the mask graph.

Step 202, obtaining the electric field distribution of the light wave behind the entrance pupil of the projection system according to the near field distribution E

The specific process of the step is as follows:

since each sub-region on the mask can be regarded as a secondary sub-light source, taking the center of the sub-region as the coordinate of the sub-region, according to the fourier optics theory, the electric field distribution in front of the projection system entrance pupil can be expressed as a 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, because of the existence of N × N sub-regions on the mask, the electric field distribution in front of the entrance pupil

Is an N × N vector matrix, each element of which is a 3 × 1 vector, representing 3 components of the electric field distribution in front of the entrance pupil in the global coordinate system. F { } denotes the fourier transform, r is the entrance pupil radius,

is the wave number, lambda is the wavelength of the light wave emitted by the point light source, n_mIs the refractive index of the object space medium.

Since the reduction ratio of the projection system is larger, generally 4 times, the numerical aperture of the object space is smaller, which results in the electric field distribution in front of the entrance pupil

Is negligible, so that the electric field distribution in front of and behind the entrance pupil of the projection system is the same, i.e.

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

Wherein, because of the existence of N × N sub-regions on the mask, the electric field distribution behind the entrance pupil

Is an N × N vector matrix, each element of which is a 3 × 1 vector representing 3 components of the electric field distribution behind the entrance pupil in the global coordinate system.

Step 203, setting the propagation direction of the light wave in the projection system to be approximately parallel to the optical axis, and further according to the electric field distribution behind the entrance pupil

Obtaining electric field distribution of light waves in front of exit pupil of projection system

The specific process of the step is as follows:

for an ideal projection system without aberrations, the mapping process of the electric field distribution behind the entrance pupil and in front of the exit pupil can be expressed in the form of a product of a low pass filter function and a correction factor, i.e.:

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

wherein the electric field distribution in front of the exit pupil

An N × N vector matrix, each element of which is a 3 × 1 vector representing 3 components of the electric field distribution in front of the exit pupil in the global coordinate system; c is a constant correction factor and the low-pass filter function U is an N × N scalar matrix representing the finite acceptance of the diffraction spectrum by the numerical aperture of the projection system, i.e. the value inside the pupil is 1 and the value outside the pupil is 0, as follows:

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

where (f, g) is the normalized global coordinate on the entrance pupil.

The constant correction factor c can be expressed as:

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

where r and r' are the projection system entrance and exit pupil radii, respectively, n_wR is the demagnification of an ideal projection system, typically 4, for the refractive index of the immersion liquid at the image side of the lithography system.

Since the propagation direction of the light waves between the entrance and exit pupils of the projection system is approximately parallel to the optical axis, the phase difference between the back of the entrance pupil and the front of the exit pupil is the same for any of (α ', β'). The constant phase difference between the back of the entrance pupil and the front of the exit pupil is negligible since the spatial image (i.e. the light intensity distribution) is ultimately required to be resolved. The electric field distribution in front of the exit pupil can thus be found to be:

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

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

Obtaining electric field distribution behind the exit pupil of a projection system

According to the rotation effect of the TM component of the electromagnetic field between the front and the back of the exit pupil, the electric field in the global coordinate system at the front and the back of the exit pupil is expressed as: vector matrix of NxN

And

and

each element of (a) is as follows:

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

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

where m, N is 1, 2,., N, α ═ cos Φ 'sin θ', β ═ sin Φ 'sin θ', γ ═ cos θ ', that is, the direction cosine (wave vector) of the plane wave incident on the image plane from the projection system exit pupil is k ═ α', β ', γ'); phi 'and theta' are the azimuth and elevation angles, respectively, of the wave vectorAnd

the relation of (A) is as follows:

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

where V is an N × N vector matrix, and each element is a 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, utilizing Wolf's optical imaging theory, according to the electric field distribution behind the exit pupil

Obtaining an electric field distribution E at a wafer location^waferAs shown in equation (7), and further obtain the mask space image I (alpha) at the position of the wafer corresponding to the 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 the inverse Fourier transform. Substituting equations (5) and (6) into equation (7) and ignoring the constant phase term, we can:

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

substituting equation (1) into equation (8) can obtain a point light source (x)_s，y_s) The light intensity distribution of the image plane when illuminated, namely:

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

due to E_i' the value of the middle element is independent of the mask coordinates, so the above equation can be written 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,

which represents a convolution of the signals of the first and second,

is an N × N vector matrix, each element being a 3 × 1 vector (v)_x′，v_y′，v_z′)^T

Then E^wafer(α_s，β_s) The three components in the global coordinate system are

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

Wherein,

p ═ x, y, z, where V_p'N x N scalar matrix' is composed of x components 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

Representing the matrix modulo and squared. Wherein H_pAnd B are both (. alpha.)_s，β_s) Are respectively marked as

And

thus the above formula can be written as:

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

if the above formula obtains the spatial image distribution corresponding to the mask under the illumination of the point light source, the spatial image of the mask under the illumination of the partially coherent light source in step 105 can be represented 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 is_sIs the number of sampling points of the partially coherent light source.

Example of implementation of the invention:

as shown in fig. 4, 401 are two point light sources a and B taken on the light source plane. 402 is the x-component of the impulse response function H of the lithographic projection system for light from different point sources at the pupil position where y is 0. 403 is the y-component of the impulse response function H of the lithographic projection system for light from different point sources at the pupil position where y is 0. 404 is the z-component of the impulse response function H of the lithographic projection system for light from different point sources at the pupil position where y is 0.

As shown in fig. 5, 501 is an initial binary mask diagram, the critical dimension of which is 45nm, white represents a light-transmitting region with a transmittance of 1, and black represents a light-blocking region with a transmittance of 0. The mask pattern is located in the xy plane with the lines parallel to the y axis. 502 is the binary mask aerial image result under ring illumination obtained after rasterizing the light source plane into 31 × 31 point light sources. 503 is the binary mask aerial image result under ring illumination obtained after the light source surface is rasterized into 2 × 2 point light sources. The intensity profiles at Y-0 obtained by the two methods are compared 504. Reference numeral 505 denotes a light intensity distribution curve obtained by rasterizing a light source plane into 31 × 31 point light sources. 506 is a light intensity distribution curve obtained by rasterizing a light source plane into 2 × 2 point light sources.

It can be seen from 402, 403 and 404 in fig. 4 that there is a large difference between the impulse response functions of the lithographic projection system for different point light sources. In this case, if the same impulse response function is used for different electric light sources, errors will inevitably be caused in obtaining the aerial image. Comparing 505 and 506 in fig. 5, it can be seen that the light intensity distribution is greatly different by using different density of the grid on the light source surface. The above results prove the importance of rasterizing the partially coherent light source and calculating the spatial image of the mask point by adopting a proper method under the ultra-large NA photoetching imaging and the significance of the invention.

Although the embodiments of the present invention have been described with reference to the accompanying drawings, it will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the invention, and these are intended to be within the scope of the invention.

Claims (4)

1. A method for obtaining a mask space image based on an Abbe vector imaging model is characterized by comprising the following specific steps:

step 101, rasterizing a mask M into N multiplied by N sub-regions;

step 102, gridding the light source surface into a plurality of point light sources according to the shape of the partial coherent light source, and using the central point coordinate (x) of each grid area_s,y_s) Representing the point light source coordinates corresponding to the grid area;

step 103, aiming at the single point light source, utilizing the coordinate (x) thereof_s,y_s) ObtainTaking the space image I (alpha) on the corresponding wafer position when the point light source is illuminated_s,β_s)；

Step 104, judging whether the space images of the positions of the wafer corresponding to all the point light sources are calculated, if so, entering step 105, otherwise, returning to step 103;

step 105, according to Abbe's method, corresponding space image I (alpha) to each point light source_s,β_s) And (4) performing superposition to obtain a space image I on the position of the wafer when the partially coherent light source is used for illumination.

2. The method of claim 1, wherein when the partially coherent light source is circular, the partially coherent light source is shaped to grid the light source area as: dividing a circular light source surface area into k +1 areas by using a central point on a light source surface as a circle center and k concentric circles with different preset radiuses, numbering the k +1 areas from the central circle area to the inside to the outside by 1-k +1, and dividing each area with the number of 2-k into a plurality of fan-shaped grid areas.

3. The method for obtaining the mask space image according to claim 2, wherein the number of the fan-shaped grid regions divided by each of the regions numbered from 2 to k is the same.

4. The method for obtaining the mask aerial image according to claim 1, wherein the specific process of the step 103 is as follows:

setting a global coordinate system as follows: taking the direction of an optical axis as a z-axis, and establishing a global coordinate system (x, y, z) by the z-axis according to the principle of a left-hand coordinate system;

step 201, according to the coordinates (x) of the point light source_s,y_s) Calculating the near-field distribution E of the light waves emitted by the point light source passing through the NxN sub-regions on the mask; wherein E is an N × N vector matrix, each element of which is a 3 × 1 vector representing 3 components of the diffracted near-field distribution of the mask in the global coordinate system;

step 202, according toThe near field distribution E acquires the electric field distribution of the light wave behind the entrance pupil of the projection system

Wherein,

a vector matrix of N × N, each element of which is a 3 × 1 vector, representing 3 components of the electric field distribution behind the entrance pupil in the global coordinate system;

step 203, setting the propagation direction of the light wave in the projection system to be approximately parallel to the optical axis, and further according to the electric field distribution behind the entrance pupil

Obtaining electric field distribution of light waves in front of exit pupil of projection system

Wherein the electric field distribution in front of the exit pupil

A vector matrix of N × N, each element of which is a 3 × 1 vector, representing 3 components of the electric field distribution in front of the exit pupil in the global coordinate system;

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

Obtaining electric field distribution behind the exit pupil of a projection system

Step 205, using Walf Wolf optical imaging theory, according to the electric field distribution behind the exit pupil

Obtaining an electric field distribution E at a wafer location^waferAnd according to E^waferObtaining an aerial image I (alpha) of the point light source corresponding to the position of the wafer_s,β_s)。

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