CN102269926B

CN102269926B - Method for optimizing optical proximity correction (OPC) of nonideal photoetching system based on Abbe vector imaging model

Info

Publication number: CN102269926B
Application number: CN2011102683288A
Authority: CN
Inventors: 马旭; 李艳秋; 董立松
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2011-09-09
Filing date: 2011-09-09
Publication date: 2012-08-15
Anticipated expiration: 2031-09-09
Also published as: CN102269926A

Abstract

The invention provides a method for optimizing optical proximity correction (OPC) of a nonideal photoetching system based on an Abbe vector imaging model. The method comprises the following steps of: setting transmittivity of an opening part and a light blocking part in a mask; setting a variable matrix Omega; setting a target function D as linear combination of an imaging evaluation function of an ideal image surface and an imaging evaluation function of an image surface of which the defocusing quantity is fnm; and guiding optimization on a mask pattern by using the variable matrix Omega and the target function D. By using the vector imaging model and taking vector characteristic of an electromagnetic field into consideration during acquisition of a space image, the optimized mask is suitable for the photoetching system with small numerical aperture (NA) and also suitable for the photoetching system of which the NA is more than 0.6. By the method, the gradient information of optimizing the target function is utilized and a steepest descent method is combined to optimize the pattern and the phase of an attenuated phase-shifting mask, so the optimization efficiency is high.

Description

Optimization method of non-ideal lithography system OPC based on Abbe vector imaging model

Technical Field

The invention relates to an optimization method of non-ideal lithography system OPC (lithography proximity correction) based on Abbe (Abbe) vector imaging model, belonging to the technical field of lithography 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, so that the mask pattern is reproduced on the wafer.

The mainstream lithography system at present is an ArF deep ultraviolet lithography system with the wavelength of 193nm, and as the node of the lithography technology enters 45nm-22nm, the key size of a circuit is far smaller than the wavelength of a light source. The interference and diffraction phenomena of the light are more pronounced, resulting in distortions and blurring of the lithographic image. For this reason, the lithography system must employ resolution enhancement techniques to improve the imaging quality. Optical proximity correction (optical proximity correction opc) is an important lithography resolution enhancement technique. 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. In the immersion lithography system, liquid with the refractive index larger than 1 is added between the lower surface of the last lens of the projection objective and a wafer, so that the aims of enlarging the numerical aperture (numerical aperture NA) and improving the imaging resolution are fulfilled. Since immersion lithography systems have the property of a high NA (NA > 1), scalar imaging models of lithography systems are no longer applicable when NA > 0.6. In order to obtain accurate imaging characteristics of an immersion lithography system, the mask in the immersion lithography system must be optimized using OPC techniques based on a vector imaging model.

In an actual lithography system, there are a number of process variations. On one hand, due to factors such as processing and adjustment, the projection system can generate certain influence on the phase of incident light, and further the imaging quality of the photoetching system is influenced, so that the photoetching system is a non-ideal photoetching system, and the influence is mainly reflected in two aspects of scalar aberration and polarization aberration of the projection system. On the other hand, due to the influence of factors such as control, the actual position of the wafer in the lithography system changes, and the actual image plane position (wafer position) deviates from the ideal image plane position of the lithography system, and this image plane deviation phenomenon appears as the image plane defocusing of the lithography system. The quality of an aerial image obtained at the actual image plane position differs greatly from that obtained at the ideal image plane. In order to design an OPC optimization scheme suitable for an actual lithography system, the influence of various process variations in the lithography system must be considered.

The related art (Journal of Optics, 2010, 12: 045601) proposes an OPC optimization method for enlarging the depth of focus of a lithography system based on a gradient for a partially coherent imaging system. However, the above method has the following two disadvantages: first, the above method is based on a scalar imaging model of the lithography system, and is therefore not suitable for high NA lithography systems. Second, the above method does not consider the influence of scalar aberration, polarization aberration, etc. of the lithography system, and is not suitable for a non-ideal lithography system.

Disclosure of Invention

The invention aims to provide an optimization method of non-ideal lithography system OPC based on an Abbe vector imaging model. The method adopts the OPC technology of a vector model to optimize the mask, and can be suitable for an immersion lithography system with high NA and a dry lithography system with low NA.

The technical scheme for realizing the invention is as follows:

an optimization method of non-ideal lithography system OPC based on Abbe vector imaging model comprises the following steps:

step 101, initializing the mask pattern M to a target pattern with size of NXN；

102, setting the transmissivity of an opening part on the initial mask graph M to be 1 and the transmissivity of a light blocking area to be 0; setting a variable matrix Ω of N × N: when M (x, y) is 1,

when M (x, y) is 0,

wherein M (x, y) represents the transmittance of each pixel point on the mask pattern;

step 103, constructing the objective function D as an imaging evaluation function D at an ideal image surface₁Image evaluation function D at image surface with defocus amount f₂Linear combination of (i), i.e. D ═ η D₁+(1-η)D₂Wherein η ∈ (0, 1) is a weighting coefficient;

imaging evaluation function D₁Set as the square of the Euler distance between the aerial image on the ideal image plane and the target pattern after amplitude modulation, i.e.

Wherein

Being a target patternPixel value, I_nom(x, y) is the pixel value of a space image on an ideal image surface corresponding to the current mask, and omega epsilon (0, 1) is an amplitude modulation coefficient;

imaging evaluation function D₂The defocus amount is set to be the square of the Euler distance between the aerial image on the f image plane and the target pattern after amplitude modulation, that is, the defocus amount is set to be the square of the Euler distance between the aerial image on the f image plane and the target pattern after amplitude modulation

Wherein I_off(x, y) is the pixel value of the space image on the f image surface corresponding to the defocusing amount of the current mask;

step 104, calculating a gradient matrix of the objective function D to the variable matrix omega

Step 105, updating the variable matrix to be omega' by using the steepest descent method, namely

Wherein s is a preset optimization step length, and a mask graph corresponding to the current omega' is obtained

Step 106, calculating the current mask pattern

The corresponding objective function value D; when D is smaller than a preset threshold value or the number of times of updating the variable matrix omega reaches a preset upper limit value, the step 107 is entered, otherwise, the variable matrix omega is enabled to be omega', and the step 104 is returned;

step 107, terminating the optimization and intercepting the current mask pattern by using the square window

Central part of (2)

The side length of the square window is the smaller of the period of the target graph in the horizontal direction and the period of the target graph in the vertical direction;

step 108, for

Periodically extending in the horizontal direction and the vertical direction until the extended mask size is larger than or equal to the target pattern size, and obtaining the pattern

And determining the optimized mask pattern.

In step 103 of the present invention, the process of obtaining the aerial image on the ideal image plane corresponding to the current mask and the aerial image on the image plane with the defocus amount f corresponding to the current mask is as follows:

step 201, rasterizing a mask pattern M into N multiplied by N sub-regions;

step 202, grid the light source surface into a plurality of point light sources, and use the central point coordinates (x) of each grid area_s，y_s) Representing the point light source coordinates corresponding to the grid area;

step 203, acquiring the variation ξ of the phase of the incident light of the lithography system caused by δ according to the distance δ between the image plane where the space image needs to be acquired and the ideal image plane; wherein δ is 0 for the aerial image on the ideal image plane, and δ is f for the aerial image on the image plane with defocus amount f;

step 204, obtaining a scalar aberration matrix W (α ', β ') describing the scalar aberration of the projection system and a polarization aberration matrix J (α ', β ') describing the polarization aberration of the projection system, wherein (α ', β ', γ ') is a coordinate system of the global coordinate system on the image plane after Fourier transformation;

step 205, for a single point light source, utilize its coordinates (x)_s，y_s) The variation xi of the incident light phase, the scalar aberration matrix W (alpha ', beta') and the polarization aberration matrix J (alpha ', beta') are obtained, and when the point light source is illuminated, a space image I on an ideal image surface is obtained_nom(α_s，β_s) And an aerial image I on the image surface with defocus f_off(α_s，β_s)；

Step 206, judging whether the space image I corresponding to all the point light sources is calculated_nom(α_s，β_s) And I_off(α_s，β_s) If yes, go to step 207, otherwise return to step 205;

step 207, according to the Abbe method, corresponding space image I to each point light source_nom(α_s，β_s) Superposing to obtain a space image I on an ideal image surface_nomFor space image I corresponding to each point light source_off(α_s，β_s) Superposing to obtain a space image I on an image surface with a defocusing amount f_off。

In step 205, an aerial image I corresponding to the point light source is obtained_nom(α_s，β_s) And I_off(α_s，β_s) The specific process comprises the following steps:

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;

301, 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 302, obtaining the electric field distribution of the light wave behind the entrance pupil of the projection system according to the near field distribution E

WhereinA 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 303, 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

Scalar aberration matrix W (α ', β') and polarization aberration matrix J (α ', β') to obtain the electric field distribution of the light waves in front of the exit pupil of the 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;

304, 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

305, utilizing the Walf Wolf optical imaging theory, according to the electric field distribution behind the exit pupilAnd the variation xi of the incident light phase to obtain the electric field distribution on the ideal image surface

And the electric field distribution on the image plane with defocus fAnd according to

Obtaining a space image I on an ideal image surface corresponding to a point light source_nom(α_s，β_s) According toObtaining a spatial image I on an image surface with defocus f corresponding to a point light source_off(α_s，β_s)。

Advantageous effects

In the process of acquiring the space image of the lithography system, the influence of scalar aberration, polarization aberration and defocus of the non-ideal lithography system is considered, so that the optimization method can be suitable for the non-ideal lithography system.

Secondly, the vector imaging model utilized in the invention considers the vector characteristic of the electromagnetic field in the process of acquiring the space image, so that the optimized mask is not only suitable for a photoetching system with small NA, but also suitable for a photoetching system with NA more than 0.6.

Thirdly, the method optimizes the mask graph by utilizing the gradient information of the optimized objective function and combining the steepest descent method, and the optimization efficiency is high.

Drawings

FIG. 1 is a flowchart illustrating an OPC optimizing method for a non-ideal lithography system based on an Abbe vector imaging model according to the present invention.

FIG. 2 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 aerial image at a wafer position.

FIG. 3 is a schematic diagram of wafer position deviation from an ideal image plane.

FIG. 4 is a schematic diagram of rasterizing a partially coherent light source plane in an embodiment of the present invention.

FIG. 5 is a schematic wavefront diagram of scalar aberrations and polarization aberrations (represented by Jones pupil) for a projection system of a particular lithography system.

FIG. 6 shows an initial mask and an optimized mask corresponding to dense lines under unpolarized illumination without aberrationMask center section cut with square window

And based on

Optimized mask after periodic continuation

Schematic representation of (a).

FIG. 7 is a diagram of an initial mask corresponding to dense lines and an optimized mask after periodic extension when there is no aberration under unpolarized illumination

Corresponding process window schematic.

FIG. 8 shows an initial mask and an optimized mask corresponding to dense lines when there is aberration under unpolarized illumination

Mask center section cut with square window

And based on

Optimized mask after periodic continuationSchematic representation of (a).

FIG. 9 is a diagram of an initial mask corresponding to dense lines and an optimized mask after periodic extension when there is aberration under unpolarized illumination

Corresponding process window schematic.

Detailed Description

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

The principle of the invention is as follows: the process variation factors in an actual lithography system mainly include: exposure variation, defocus, scalar aberration, polarization aberration, and the like. The scalar aberration and the polarization aberration mainly affect the phase of the incident light of the projection system, and after the used lithography system is determined, the scalar aberration and the polarization aberration of the projection system can be obtained by using a ray tracing method. The stability of the lithography system to exposure variation and defocus can be evaluated using a process window. The horizontal axis of the process window is the defocus Depth (Depth of focus DOF), which represents the maximum difference between the actual wafer position and the ideal image plane on the premise that the imaging quality is acceptable. The vertical axis of the process window is Exposure depth (EL), which represents the acceptable Exposure variation range under the premise of acceptable imaging quality; EL is typically expressed as the amount of change in exposure as a percentage of the nominal exposure. The opening of the process window contains all the corresponding combinations of DOF and EL that meet the specific manufacturing process requirements. The specific manufacturing process requirements generally include Critical Dimension (CD) errors, sidewall angles of the imaged contours in the photoresist, and other parameters. When the process window opening corresponding to the photoetching system is large, the stability of the system to exposure variation and defocusing is high.

To expand the process window opening in the transverse axis (DOF) direction, i.e., to expand the gap between the actual wafer position and the ideal image plane, provided that the imaging quality is acceptable. The invention constructs a target function D as an imaging evaluation function D at an ideal image surface₁Image evaluation function D at image surface with defocus amount f₂Linear combination of (i), i.e. D ═ η D₁+(1-η)D₂Where η ∈ (0, 1) is a weighting coefficient.

In order to enlarge the process window opening in the direction of the longitudinal axis (EL), i.e. to enlarge the acceptable range of exposure variation, provided that the imaging quality is acceptable. The method of the invention should make the space image corresponding to the optimized OPC as close as possible to the target graph. The reason for this is that: when the aerial image is close to the target graph, the aerial image distribution has a relatively steep side wall angle, so that the relatively steep side wall angle of the imaging contour in the photoresist is favorably formed; meanwhile, the line width difference of the space image distributed on the cross sections with different heights is small, and the CD error caused by the change of the exposure can be reduced. Assuming that the size of the target pattern is NXN, the imaging evaluation function D of the invention₁Set as the square of the Euler distance between the aerial image on the ideal image plane and the target pattern after amplitude modulation, i.e.

Wherein

Is the pixel value of the target pattern, I_nomAnd (x, y) is the pixel value of a space image on the ideal image surface corresponding to the current mask, and omega epsilon (0, 1) is an amplitude modulation coefficient. Imaging evaluation function D₂The defocus amount is set to be the square of the Euler distance between the aerial image on the f image plane and the target pattern after amplitude modulation, that is, the defocus amount is set to be the square of the Euler distance between the aerial image on the f image plane and the target pattern after amplitude modulation

Wherein I_offAnd (x, y) is the pixel value of the space image on the image plane, which is the defocus amount corresponding to the current mask.

As shown in FIG. 1, the method for optimizing the OPC of the non-ideal lithography system based on the Abbe vector imaging model comprises the following specific steps:

step 101, initializing the mask pattern M to a target pattern with size of NXN

。

when M (x, y) is 0,

where M (x, y) represents the transmittance of each pixel on the mask pattern.

Step 103, constructing the objective function D as an imaging evaluation function D at an ideal image surface₁Image evaluation function D at image surface with defocus amount f₂Linear combination of (i), i.e. D ═ η D₁+(1-η)D₂Where η ∈ (0, 1) is a weighting coefficient.

Wherein

Is the pixel value of the target pattern, I_nomAnd (x, y) is the pixel value of a space image on the ideal image surface corresponding to the current mask, and omega epsilon (0, 1) is an amplitude modulation coefficient.

Imaging evaluation function D₂Set the defocus amount to be f space image on image surface and the amplitude modulatedSquares of Euler distances between target patterns, i.e.

variable predefinition

As shown in fig. 2, 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:

α_s＝x_s·NA_m，β_s＝y_s·NA_m，

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 transformation 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 (4) carrying out a coordinate system after Fourier transformation.

Conversion relationship between global coordinate system and local coordinate system:

establishing a local coordinate system (e)_⊥，e_P)，e_⊥The axis being the direction of vibration of the TE-polarized light in the light emitted by the light source, e_PThe 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:

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:

wherein,

in an actual lithography system, there is a phenomenon in which the position of the wafer deviates from an ideal image plane, and the distance between the two is represented by δ. As shown in fig. 3. 301 is the distance from the actual position of the wafer to the ideal image plane, and its effect on the image is reflected in the change of the optical path length, as shown in 302, which can be obtained from the geometrical relationship:

Optical_pach＝n_wδ(1-cosθ)

wherein n is_wTheta is the refractive index of the immersion liquid at the image side of the lithography system, and theta is the angle between the light ray and the optical axis.

The acquisition process of the aerial image is as follows:

step 201, the mask pattern M is rasterized into N × N sub-regions.

Step 202, grid the light source surface into a plurality of areas, each area is approximated by a point light source, and the center point coordinate (x) of each grid area_s，y_s) And representing the point light source coordinates corresponding to the grid area. As shown in fig. 4, the method of the present invention uses equally spaced lines parallel to the X-axis and Y-axis directions to grid the light source plane of a partially coherent light source into small squares of equal size.

Step 203, acquiring the variation ξ of the phase of the incident light of the lithography system caused by δ according to the distance δ between the image plane where the space image needs to be acquired and the ideal image plane; where δ is 0 for an aerial image on an ideal image plane, and δ is f for an aerial image on an image plane with defocus amount f.

Because the actual position of a wafer in the photoetching system changes under the influence of factors such as control and the like, the actual image plane position deviates from the position of an ideal image plane of the photoetching system, and defocusing amount is generated; the defocusing amount can bring the phase change of the incident light of the photoetching system, and the variable quantity xi is

Wherein

Is the wave number.

When the space image on the ideal image surface is solved, delta is equal to 0, the solved defocusing amount is the space image on the f image surface, and delta is equal to f.

Step 204, obtaining a scalar aberration matrix W (α ', β ') and a polarization aberration matrix J (α ', β ') of the projection system, wherein (α ', β ', γ ') is a coordinate system of the global coordinate system on the image plane after fourier transformation.

The projection system is a non-ideal optical system due to processing, adjustment and other factors, and the phase of incident light is also affected to a certain extent. For low numerical aperture projection systems, only the scalar aberration matrix W (α ', β') is needed to describe the non-idealities of the projection system, assuming that the optical wavefront has the same amplitude over the entire pupil of the projection system. However, as the numerical aperture of the projection system increases, the vector imaging property of the light wave has a more significant effect on the aerial image at the wafer position, and therefore the present invention further considers the effect of the polarization aberration J (α ', β') on the aerial image at the wafer position.

The scalar aberration matrix W (α ', β') and the polarization aberration matrix J (α ', β') are each N × N matrices; each element in the W (α ', β') matrix is a numerical value that represents the number of wavelengths that the actual wave surface at the exit pupil differs from the ideal wave surface; j (α ', β') is an N × N vector matrix, each matrix element is a Jones matrix, and since TE and TM polarized light pass through the transformation matrix, both expressed in the form of xy components, the Jones matrix is specifically formed as:

m，n＝1，2，...，N

J_i′，j' (α ', β ', m, n) (i ' ═ x, y; j ' ═ x, y) denotes the ratio of incident i ' polarized light to j ' polarized light after passing through the projection system.

Step 205, for a single point light source, utilize its coordinates (x)_s，y_s) The variation xi of the incident light phase, the scalar aberration matrix W (alpha ', beta') and the polarization aberration matrix J (alpha ', beta') are obtained, and when the point light source is illuminated, a space image I on an ideal image surface is obtained_nom(α_s，β_s) And an aerial image I on the image surface with defocus f_off(α_s，β_s)。

Step 206, judging whether the space image I corresponding to all the point light sources is calculated_nom(α_s，β_s) And I_off(α_s，β_s) If yes, go to step 207, otherwise return to step 205.

In step 205, an aerial image I is obtained_nom(α_s，β_s) And I_off(α_s，β_s) The specific process comprises the following steps:

301, 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 3 × 1 vector, which represents 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:

<math> <mrow> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>j</mi> <mn>2</mn> <mi>π</mi> <msub> <mi>β</mi> <mi>s</mi> </msub> <mi>m</mi> <mo>×</mo> <mi>pixel</mi> </mrow> <mi>λ</mi> </mfrac> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>j</mi> <mn>2</mn> <mi>π</mi> <msub> <mi>α</mi> <mi>s</mi> </msub> <mi>n</mi> <mo>×</mo> <mi>pixel</mi> </mrow> <mi>λ</mi> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>

1, 2, wherein pixel represents on the mask patternThe side length of each sub-region.

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:

wherein, because of the existence of N × N sub-regions on the mask, the electric field distribution in front of the entrance pupil

Vector of NxNA quantity matrix, each element of which is a 3 × 1 vector, representing 3 components of the electric field distribution in the global coordinate system in front of the entrance pupil. 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.

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.

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.:

wherein the electric field distribution in front of the exit pupilAn 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:

<math> <mrow> <mi>U</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <msqrt> <msup> <mi>f</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>g</mi> <mn>2</mn> </msup> </msqrt> <mo>≤</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>elsewhere</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

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

The constant correction factor c can be expressed as:

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'). Since it is ultimately required to solve the aerial image (i.e., the light intensity distribution) on the wafer, the constant phase difference between the back of the entrance pupil and the front of the exit pupil is negligible. The electric field distribution in front of the exit pupil can thus be found to be:

because the projection system is a non-ideal optical system caused by factors such as processing and adjustment, the electric field distribution in front of the exit pupil of the non-ideal lithography system is obtained according to the electric field distribution in front of the exit pupil of the ideal lithography system by considering the influence of scalar aberration W (alpha ', beta') and polarization aberration J (alpha ', beta'),

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:

where m, N is 1, 2, as, 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 set to be equal toPhi 'and theta' are the azimuth and elevation angles, respectively, of the wave vector

And

the relation of (A) is as follows:

where V is an N × N vector matrix, and each element is a 3 × 3 matrix:

m，n＝1，2，...，N

step 305, utilize WoThe theory of optical imaging of the Lev Wolf is based on the electric field distribution behind the exit pupilObtaining electric field distribution on ideal image surface

And according toObtaining space image I of point light source corresponding to ideal image surface_nom(α_s，β_s)。

According to the electric field distribution behind the exit pupil by using Walf Wolf optical imaging theory

And the variation xi of the incident light phase, and acquiring the defocusing amount as the electric field distribution on the f image surface

And according to

Obtaining a space image I on an image surface with f defocusing amount corresponding to a point light source_off(α_s，β_s)。

The specific process of the step is as follows:

when the variation ξ of the phase of the incident light of the lithography system caused by the defocus δ of the non-ideal lithography system is not considered, the electric field distribution at the wafer position is shown as the formula (7):

<math> <mrow> <msup> <mover> <mi>E</mi> <mo>^</mo> </mover> <mi>wafer</mi> </msup> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>πλ</mi> <msup> <mi>r</mi> <mo>′</mo> </msup> </mrow> <msubsup> <mi>jn</mi> <mi>w</mi> <mn>2</mn> </msubsup> </mfrac> <msup> <mi>e</mi> <mrow> <mi>j</mi> <msup> <mi>k</mi> <mo>′</mo> </msup> <msup> <mi>r</mi> <mo>′</mo> </msup> <msup> <mi>F</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </msup> <mo>{</mo> <mfrac> <mn>1</mn> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mfrac> <msubsup> <mi>E</mi> <mi>b</mi> <mi>ext</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,f-1{ } is an inverse Fourier transform. Substituting equations (5) and (6) into equation (7) and ignoring the constant phase term, we can:

<math> <mrow> <msup> <mover> <mi>E</mi> <mo>^</mo> </mover> <mi>wafer</mi> </msup> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <msub> <mi>n</mi> <mi>w</mi> </msub> <mi>R</mi> </mrow> </mfrac> <msup> <mi>F</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>{</mo> <msqrt> <mfrac> <mi>γ</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mfrac> </msqrt> <mi>eVeUe J</mi> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>β</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>eF</mi> <mo>{</mo> <mi>E</mi> <mo>}</mo> <mi>e</mi> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>πW</mi> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>β</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> </mrow> </msup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

for a non-ideal lithography system, when there is a distance δ between the image plane of the computed aerial image and the ideal image plane, it is necessary to consider the influence of the δ -induced phase change ξ of the incident light of the lithography system.

The electric field distribution on the non-ideal lithography system is then:

<math> <mrow> <msup> <mi>E</mi> <mi>wafer</mi> </msup> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>πλ</mi> <msup> <mi>r</mi> <mo>′</mo> </msup> </mrow> <msubsup> <mi>jn</mi> <mi>w</mi> <mn>2</mn> </msubsup> </mfrac> <msup> <mi>e</mi> <mrow> <mi>j</mi> <msup> <mi>k</mi> <mo>′</mo> </msup> <msup> <mi>r</mi> <mo>′</mo> </msup> </mrow> </msup> <msup> <mi>F</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>{</mo> <mfrac> <msup> <mi>e</mi> <mi>jξ</mi> </msup> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mfrac> <mi>e</mi> <msubsup> <mi>E</mi> <mi>b</mi> <mi>ext</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

let δ be f, then

The defocus amount is the electric field distribution on the f image plane.

Let δ equal 0, then The electric field distribution on the ideal image surface.

When the formulas (1), (5) and (6) are substituted into the formula (9), a point light source (. alpha.) can be obtained_s，β_s) The light intensity distribution of the image plane when illuminated, namely:

<math> <mrow> <msup> <mi>E</mi> <mi>wafer</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <msub> <mi>n</mi> <mi>w</mi> </msub> <mi>R</mi> </mrow> </mfrac> <msup> <mi>F</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>{</mo> <msqrt> <mfrac> <mi>γ</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mfrac> </msqrt> <mi>e</mi> <msup> <mi>e</mi> <mi>jξ</mi> </msup> <mi>eVeUeJ</mi> <mrow> <mo>(</mo> <mrow> <mo></mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <msup> <mi>β</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mi>eF</mi> <mo>{</mo> <msub> <mi>E</mi> <mi>i</mi> </msub> <mmultiscripts> <mi>e</mi> <mo>′</mo> </mmultiscripts> <mi>BeM</mi> <mo>}</mo> <mi>e</mi> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>πW</mi> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>β</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> </mrow> </msup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

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

<math> <mrow> <msup> <mi>E</mi> <mi>wafer</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <msub> <mi>nw</mi> <mi>R</mi> </msub> </mfrac> <msup> <mi>F</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>{</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo>}</mo> <mo>&CircleTimes;</mo> <mrow> <mo>(</mo> <mi>BeM</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein

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

<math> <mrow> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo>=</mo> <msqrt> <mfrac> <mi>γ</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mfrac> </msqrt> <mi>e</mi> <msup> <mi>e</mi> <mrow> <mi>jξ</mi> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>β</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> </mrow> </msup> <mi>eVeUeJ</mi> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>β</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>e</mi> <msub> <mi>E</mi> <mi>i</mi> </msub> <mmultiscripts> <mi>e</mi> <mo>′</mo> </mmultiscripts> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>πW</mi> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>β</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </math>

is an N × N vector matrix, each matrix element is a 3 × 1 vector (v)_x′，v_y′，v_z′)^TWherein v is_x′，v_y′，v_z' is a function of both alpha ' and beta '.

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

<math> <mrow> <msubsup> <mi>E</mi> <mi>P</mi> <mi>wafer</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>H</mi> <mi>p</mi> </msub> <mo>&CircleTimes;</mo> <mrow> <mo>(</mo> <mi>BeM</mi> <mo>)</mo> </mrow> </mrow> </math>

Wherein,

p is x, y, z, where Vp 'is an N × N scalar matrix composed of x components of elements of the vector matrix V'.

<math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>Σ</mi> <mrow> <mi>p</mi> <mo>=</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>x</mi> </mrow> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>H</mi> <mi>p</mi> </msub> <mo>&CircleTimes;</mo> <mrow> <mo>(</mo> <mi>BeM</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

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:

<math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msub> <mtext>α</mtext> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>Σ</mi> <mrow> <mi>p</mi> <mo>=</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>x</mi> </mrow> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>H</mi> <mi>p</mi> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <msub> <mi>β</mi> <mi>s</mi> </msub> </mrow> </msubsup> <mo>&CircleTimes;</mo> <mrow> <mo>(</mo> <msup> <mi>B</mi> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <msub> <mi>β</mi> <mi>s</mi> </msub> </mrow> </msup> <mi>eM</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

order to

If the coefficient δ is f, then I_off(α_s，β_s)＝I(α_s，β_s) (ii) a Order to

When the coefficient δ is 0, then I_nom(α_s，β_s)＝I(α_s，β_s)。

The space image I on the ideal image surface corresponding to the point light source is obtained by the above formula_nom(α_s，β_s) And a space image I on an image surface with defocusing amount f corresponding to the point light source_off(α_s，β_s) (ii) a According to the Abbe principle, then in step 207, the space image I on the ideal image surface under the illumination of the partial coherent light source_nomAnd an aerial image I on the image plane with defocus f_offCan be expressed as:

order to

When the coefficient δ is 0, then

<math> <mrow> <msub> <mi>I</mi> <mi>nom</mi> </msub> <mo>=</mo> <mi>I</mi> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>N</mi> <mi>s</mi> </msub> </mfrac> <munder> <mi>Σ</mi> <msub> <mi>α</mi> <mi>s</mi> </msub> </munder> <munder> <mi>Σ</mi> <msub> <mi>β</mi> <mi>s</mi> </msub> </munder> <munder> <mi>Σ</mi> <mrow> <mi>p</mi> <mo>=</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> </mrow> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>H</mi> <mi>p</mi> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <msub> <mi>β</mi> <mi>s</mi> </msub> </mrow> </msubsup> <mo>&CircleTimes;</mo> <mrow> <mo>(</mo> <msup> <mi>B</mi> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <msub> <mi>β</mi> <mi>s</mi> </msub> </mrow> </msup> <mi>eM</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

Order to

If the coefficient δ is f, then

<math> <mrow> <msub> <mi>I</mi> <mi>off</mi> </msub> <mo>=</mo> <mi>I</mi> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>N</mi> <mi>s</mi> </msub> </mfrac> <munder> <mi>Σ</mi> <msub> <mi>α</mi> <mi>s</mi> </msub> </munder> <munder> <mi>Σ</mi> <msub> <mi>β</mi> <mi>s</mi> </msub> </munder> <munder> <mi>Σ</mi> <mrow> <mi>p</mi> <mo>=</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> </mrow> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>H</mi> <mi>p</mi> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <msub> <mi>β</mi> <mi>s</mi> </msub> </mrow> </msubsup> <mo>&CircleTimes;</mo> <mrow> <mo>(</mo> <msup> <mi>B</mi> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <msub> <mi>β</mi> <mi>s</mi> </msub> </mrow> </msup> <mi>eM</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

Wherein N is_sIs the number of sampling points of the partially coherent light source. If TE polarized illumination is used, equation (2) is set as:

the obtained aerial image at the wafer position is I ═ I_TE. If TM polarized illumination is used, equation (2) is set as:

the obtained aerial image at the wafer position is I ═ I_TM. If unpolarized illumination is used, the aerial image at the wafer location is

；

In the invention, the gradient matrix of the objective function D to the variable matrix omega

Can be calculated as:

wherein,

(12)

wherein,^*to express a conjugate fortuneCalculating;^οindicating that the matrix is rotated 180 degrees in both the transverse and longitudinal directions.

The expression (2) can be set as follows:

and (6) derivation and calculation.The expression (2) can be set as follows:

and (6) derivation and calculation. When TE polarized illumination is used, ρ_TE＝2，ρ _TM0; when TM polarized illumination is used, ρ_TE＝0，ρ _TM2; when unpolarized illumination is used, ρ_TE＝1，ρ_TM1. Is calculated by the formula (12)

In this case, δ in equation (9) is set to 0, and the gradient of the imaging evaluation function corresponding to the ideal image plane is calculated. (11) In the formula

The formula (2) is the same as the formula (12), but δ in the formula (9) is set to f, so that the gradient of the imaging evaluation function at the image plane corresponding to the defocus amount f is calculated.

s is a preset optimization step length. Further obtaining the mask pattern corresponding to the current omega

In the course of the OPC optimization process,

has a value range of

The value range of omega (x, y) is omega (x, y) epsilon [ - ∞, + ∞]。

Step 106, calculating the current mask pattern

The corresponding objective function value D; and when the D is smaller than a preset threshold value or the number of times of updating the variable matrix omega reaches a preset upper limit value, the step 107 is entered, otherwise, the variable matrix omega is enabled to be omega', and the step 104 is returned.

Step 107, terminating the optimization, and intercepting the current mask pattern by using a square window

Central part of (2)

The side length of the square window is the smaller of the period of the target graph in the horizontal direction and the period of the target graph in the vertical direction.

Step 108, pair

And determining the optimized mask pattern.

Example of implementation of the invention:

as shown in FIG. 5, the projection system using the laboratory design in the simulation is viewed off-axisThe aberration at the field points is obtained by ray tracing (since in the field of numerical computation a two-dimensional graph is essentially a matrix-here, in effect, a two-dimensional wave surface map is drawn corresponding to a scalar aberration matrix, with the values at each coordinate point on the map corresponding one-to-one to the values of the elements of the matrix). 501 is a diagram of the aberration of the field point scale, and 502-509 are 8 Jones pupil components of the polarization aberration of the field point. 502. 503 are each J_xxReal and imaginary parts of (c). 504. 505 are respectively J_xyReal and imaginary parts of (c). 506. 507 are respectively J_yxReal and imaginary parts of (c). 508. 509 are each J_yyReal and imaginary parts of (c).

As shown in FIG. 6, when there is no aberration under unpolarized illumination, the initial mask and the optimized mask corresponding to dense lines

Mask center section cut with square window

And based on

Optimized mask after periodic continuation

Schematic representation of (a). 601 is an initial binary mask diagram with a critical dimension of 90nm, white for clear areas with a refractive index of 1, and gray for block areas with a refractive index of 0. The mask pattern lies in the XY plane with the lines parallel to the Y axis. 602 is the mask pattern optimized by the method of the present invention 603 denotes the central part of the mask, cut with a square window

604 are based onOptimized mask after periodic continuation

Corresponding process window schematic. 701 is a process window corresponding to the initial mask, and 702 is an optimized mask after periodic continuation

Corresponding process window.

As shown in FIG. 8, when there is aberration under unpolarized illumination, the initial mask and the optimized mask corresponding to dense lines

Mask center section cut with square window

And based on

Optimized mask after periodic continuation

Schematic representation of (a). 801 is an initial binary mask diagram with a critical dimension of 90nm, white for clear areas with a refractive index of 1 and gray for block areas with a refractive index of 0. The mask pattern lies in the XY plane with the lines parallel to the Y axis. 802 is the mask pattern optimized by the method of the present invention

803 denotes the central part of the mask, cut with a square window

804 are based on

Optimized mask after periodic continuation

Corresponding process window schematic. 901 is the process window corresponding to the initial mask, 902 is the optimized mask after periodic continuationCorresponding process window.

Comparing 701, 702, 901 and 902, it can be known that the method of the present invention can effectively enlarge the process window under the condition of aberration and no aberration, that is, effectively improve the stability of the lithography system to the process variation factors such as exposure variation, defocus, scalar aberration and polarization aberration.

Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, it will be understood that many variations, substitutions and modifications may be made by those skilled in the art without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims

1. An OPC optimization method based on an Abbe vector imaging model non-ideal lithography system is characterized by comprising the following specific steps:

step 101, initializing the mask pattern M to a target pattern with size of NXN

；

102, setting the transmissivity of an opening part on the initial mask graph M to be 1 and the transmissivity of a light blocking area to be 0; setting a variable matrix Ω of N × N: when M (x, y) ═ MWhen the pressure of the mixture is 1, the pressure is lower,

when M (x, y) is 0,

step 103, constructing the objective function D as an imaging evaluation function D at an ideal image surface₁Image evaluation function D at image surface with defocus amount f₂Linear combination of (i), i.e. D ═ η D₁+(1-η)D₂Wherein, eta belongs to (0, 1) as a weighting coefficient;

Wherein

Is the pixel value of the target pattern, I_nom(x, y) is the pixel value of a space image on an ideal image surface corresponding to the current mask, and omega epsilon (0, 1) is an amplitude modulation coefficient;

the process for acquiring the space image on the image surface of the projection objective corresponding to the current mask and the space image on the image surface with the defocus amount f corresponding to the current mask is as follows:

step 201, rasterizing a mask pattern M into N multiplied by N sub-regions;

step 202, grid the light source surface into a plurality of point light sources,using the center point coordinates (x) of each grid area_s，y_s) Representing the point light source coordinates corresponding to the grid area;

step 207, according to the Abbe method, corresponding space image I to each point light source_nom(α_s，β_s) Superposing to obtain a space image I on an ideal image surface_nomFor space image I corresponding to each point light source_off(α_s，β_s) Superposing to obtain a space image I on an image surface with a defocusing amount f_off；

；

Step 105, using the steepest descent methodUpdating the variable matrix to omega', i.e.

Step 106, calculating the current mask pattern

Central part of (2)

step 108, for

And determining the optimized mask pattern.

2. The optimization method of claim 1, wherein in the step 205, an aerial image I corresponding to the point light source is obtained_nom(α_s，β_s) And I_off(α_s，β_s) The specific process comprises the following steps:

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;

Wherein the electric field distribution in front of the exit pupil

Vector moment of NxNAn array, each element of which is a 3 x 1 vector, representing 3 components of the electric field distribution in the global coordinate system in front of the exit pupil;

305, utilizing the Walf Wolf optical imaging theory, according to the electric field distribution behind the exit pupil

And the variation xi of the incident light phase to obtain the electric field distribution on the ideal image surface

And the electric field distribution on the image plane with defocus f

And according to

Obtaining a space image I on an ideal image surface corresponding to a point light source_nom(α_s，β_s) According to

Obtaining a spatial image I on an image surface with defocus f corresponding to a point light source_off(α_s，β_s)。

3. The optimization method of claim 1, wherein the step 202 of rasterizing the light source area into a plurality of point light sources is: the light source surface of the partially coherent light source is rasterized into small squares of equal size with equally spaced lines parallel to the X-axis and Y-axis directions.