CN104133348B - A kind of adaptive optical etching system light source optimization method - Google Patents

Abstract

The invention provides a kind of adaptive optical etching system light source optimization method, reach and optimize light source figure, improve etching system imaging performance, and reduce the object of light source complexity as far as possible.This method adopts recursive least square method of estimation, adopts a points of measurement certificate in critical area in each iteration, upgrades current light source figure.After all observation stations of traversal, adopt reverse rank recurrence least square method of estimation, cycline rule is carried out to light source figure.Adopt this method, if obtain newly-increased the points of measurement certificate after light source optimization terminates, can directly revise current light source optimum results, and without the need to again optimizing light source.Meanwhile, the present invention can realize the parallel processing of illumination interaction coefficent matrix computations and light source optimization, and can while reduction light source complexity, the image quality of raising or maintenance etching system as far as possible.Finally, the present invention adopts vector imaging model, can meet the simulation accuracy requirement of high NA etching system.

Description

Light source optimization method of self-adaptive photoetching system

Technical Field

The invention relates to a light source optimization method of an adaptive lithography system by adopting sequential least square estimation (SELSE) and reverse Order Recursive Least Square Estimation (ORLSE), belonging to the technical field of lithography resolution enhancement.

Background

The current very large scale integrated circuit is mainly manufactured by adopting a 193nm ArF deep ultraviolet lithography system, and with the continuous reduction of Critical Dimension (CD) of the integrated circuit and the continuous improvement of integration level, Resolution Enhancement Technology (RET) must be adopted to improve the imaging resolution and the pattern fidelity of the lithography system. Light Source Optimization (SO) is an important lithography resolution enhancement technique. The SO technology modulates the light intensity and direction of light rays entering the mask by optimizing the light intensity distribution of the light source, thereby improving the imaging performance corresponding to each key area (hotspot) in the circuit pattern of the whole chip. The key area is an area which is difficult to keep high figure fidelity on an image plane within a certain process variation range. A full-chip circuit pattern typically includes a large number of critical areas with different geometric features. However, with the continuous reduction of the critical dimension of the integrated circuit, the continuous increase of the integration level and the overall dimension, and the introduction of the vector imaging model with higher simulation precision, the existing SO technology faces the problems of greatly increased data processing amount and calculation complexity, and lower operation efficiency. On the other hand, recently related researchers have implemented pixelated SO technology using freeform diffractive optical elements (DOE for short) and micro-mirror arrays. Compared with the traditional parameterized SO technology, the pixelated SO technology greatly improves the degree of freedom of light source optimization, thereby being capable of more effectively improving the imaging performance of the photoetching system. However, the light source optimization results obtained by the pixelated SO technology tend to have higher complexity, thereby reducing the manufacturability of the light source. Therefore, how to reduce the complexity of the optimized light source and improve the manufacturability of the light source becomes one of the important issues in the pixelated SO technology.

The related art (OpticsExpress,2014,22(12):14180 and 14198) adopts a Compressed Sensing (CS) technology to provide an SO method with high operation efficiency. According to the method, a plurality of observation points are calibrated at the wafer, and the images at the observation points are close to a target image as much as possible through SO optimization, SO that the imaging quality on the whole image surface is improved. The method adopts a photoetching system space imaging model as follows:whereinIs a vector of the aerial image intensity values at all pixel points on the wafer,a vector obtained by scanning the light source pattern line by line is referred to as a light source vector, and the ICC is an Illumination Cross Coefficient (ICC) matrix. The method needs to firstly calculate a complete ICC matrix, and then optimize the light source according to the imaging model. Therefore, the above method has the following two disadvantages: firstly, before optimizing the light source, the method must detect all key areas in the full-chip circuit pattern, select observation points for all key areas, and then calculate a complete ICC matrix corresponding to all observation points. After the light source optimization is finished, once a new key area and an observation point are detected, the original light source optimization result is no longer the optimal result for the newly added key area and the newly added observation point. Therefore, we must expand the original ICC matrix to include the data of the newly added key regions and observation points, and then re-optimize the light source. Therefore, the newly added key region and observation point data will result in a large amount of repeated optimization calculations. Secondly, the ICC matrix has high computational complexity and consumes a long time, and the method needs to compute a complete ICC matrix before optimizing the light source, so that the ICC matrix and the light source cannot be computed simultaneously in a parallel computing manner, thereby limiting further improvement of the arithmetic efficiency of the algorithm. In summary, the existing SO method cannot adaptively update the existing light source optimization result according to the newly added key area and observation point, and cannot realize parallel processing of ICC matrix calculation and light source optimization, which needs to be further improved.

On the other hand, the related art (applied optics,2013,52(18):4200-4211) proposes a regularization method for reducing the complexity of the light source optimization result. After the optimization of the light source is finished, firstly, all light source pixel points with the light intensity smaller than a preset threshold value are set to be 0. And then, circularly traversing all the light source pixels, and for each light source pixel, if the number of non-zero pixels in 8 light source pixels adjacent to the light source pixel is less than 3, setting the light source pixel to be 0. However, the method does not consider the influence of the simplification of the light source on the imaging performance of the photoetching system while reducing the complexity of the light source pattern. Therefore, the existing light source regularization method is difficult to improve or maintain the imaging quality of the lithography system while reducing the complexity of the light source, and needs to be further improved.

Disclosure of Invention

The invention aims to provide a light source optimization method of an adaptive photoetching system by adopting SELSE and reverse ORLSE, which converts the SO optimization problem into the signal estimation problem, thereby achieving the purposes of regularizing a light source graph and reducing the complexity of a light source. The technical scheme for realizing the invention is as follows:

a light source optimization method of a self-adaptive photoetching system comprises the following specific steps:

step 101, initializing a light source to a size of N_S×N_SLight source pattern J, mask pattern M and target patternGraph rasterized to N × N, initialized with size N_S ²×N_S ²The SELSE covariance matrix sigma, initializing the variance σ of the noise vector²Initializing ICC matrix to be a null matrix, recording as ICC, and vectorInitialized to a null vector, where N_SAnd N is an integer;

102, scanning the light source graph J line by line from top left to bottom right, and converting the J into N_S ²× 1 light source vector The element value of (b) is a pixel value of the light source pattern J;

step 103, calculating each light sourcePixel point (x)_s,y_s) Corresponding x-axis component equivalent point spread functiony-axis component equivalent point spread functionAnd z-axis component equivalent point spread function

Step 104, selecting a new observation point in a critical area on the waferSelecting vectorsMiddle corresponding observation pointElement z of^s(ii) a Calculating corresponding observation pointsNew row of the ICC matrixIts size is 1 × N_S ²Wherein T is a transpose operation; will be provided withSupplementing the current ICC matrix as the lowest row; will z^sAs a last element to supplement the currentVector is carried out;

step 105, updating the light source vector by adopting SELSE method

Step 106, if there are new observation points on the wafer, returning to step 104; otherwise, go to step 107;

step 107, calculating the regularized light source vector by adopting a reverse ORLSE method

Step 108, the light source vector after the regularization is carried outPerforming a reverse scan operation onEach element value in (1) is assigned to a corresponding N_S×N_SAnd setting other pixels on the light source pattern to 0, and recording the obtained light source pattern asNamely the optimized light source pattern.

Step 103 of the present invention calculates a light source pixel (x)_s,y_s) Corresponding equivalent point spread function Andthe method comprises the following specific steps:

setting the direction of the optical axis as the z-axis, and establishing a global coordinate system according to the principle of the left-hand coordinate system, (α, gamma) is the coordinate system of the global coordinate system (x, y, z) on the mask after Fourier transform, (α ', β ', gamma ') is the coordinate system on the waferGlobal coordinate system (x)_w,y_w,z_w) A coordinate system after Fourier transform;

step 201, aiming at a single point light source (x)_s,y_s) Calculating the vector matrix of N × NEach element being equal toRepresenting a point source (x)_s,y_s) An electric field vector of an electric field emitting the light wave in a global coordinate system;

step 202, for a single point light source (x)_s,y_s) Calculating the electric field vector rotation matrix from the front of the exit pupil to the back of the exit pupilWhereinIs a vector matrix of size N × N, each element being a matrix of 3 × 3, which can be calculated from (α ', β ', γ ');

step 203, aiming at a single point light source (x)_s,y_s) Calculating the vector matrix of N × NWhere U is the pupil filtering function and,is a vector of 3 × 1 for each element ofm,n＝1,...N；

Step 204, respectively extractingEach element inX-direction component of pixelComponent in y directionAnd the z-direction componentObtaining three scalar matrices of size N × NAnd

step 205, byAndcalculating light source pixel (x)_s,y_s) Corresponding equivalent point spread functionAnd

step 104 of the present invention calculates the corresponding observation pointsNew row of the ICC matrixThe method comprises the following specific steps:

step 301, rasterizing a light source pattern J into N_S×N_SA plurality of pixels, each pixel serving as a point light source;

step 302, for a single point light source (x)_s,y_s) Obtaining observation points on the corresponding wafer when the point light source is illuminatedIntensity of aerial image of

Step 303, determining whether all the point light sources have been calculated, corresponding to the observation pointsIf yes, go to step 304, otherwise go back to step 302;

step 304, scanning the light source graph J line by line from top left to bottom right, and illuminating all the point light sources according to the scanning sequence, wherein the observation points correspond to the point light sourcesIs arranged to have a size of 1 × N_S ²Vector of (2)And takes it as the corresponding observation pointA new row of the ICC matrix.

In step 105, the invention updates the light source vector by using a SELSE methodThe specific process comprises the following steps:

step 401, calculate the size N_S ²× 1 gain factorThe current SELSE covariance matrix is recorded as Σ [ n-1 ]]Update Σ toWherein I is an identity matrix;

step 402, recording the current light source vector asThe light source vector is updated as:

step 403, calculating a light source vectorAnd is noted as the minimum element value of

Step 404, update σ as:whereinRepresenting light source vectorThe minimum element value in (c), omega > 1 is a preset amplification factor;

step 405, ifStep 106 is entered, otherwise step 406 is entered;

step 406, calculate the size N_S ²× 1 gain factorUpdate sigma toWherein I is an identity matrix;

step 407, updating the light source vector to:and will beAll the pixel values smaller than 0 are set to 0.

In step 107, the invention adopts a reverse ORLSE method to calculate the regularized light source vectorThe specific process comprises the following steps:

step 501, assuming that the total number of currently selected observation points is K, the size of the current ICC matrix is K × N_S ²Current vectorSize of K × 1, from size N_S ²× 1 light source vectorFinds all elements with value equal to 0, and removes these elements fromDeleting to obtain new light source vector with W × 1 sizeDeleting the columns in the ICC matrix corresponding to the elements from the ICC matrix to obtain a new ICC matrix with the size of K × W, which is recorded as ICC^sWherein W is the light source vectorThe number of all elements greater than 0; setting the loop variable to be 0;

step 502, determining a light source vectorElement j having the minimum value of_minIf j is_min<t_sAnd loop < loop_maxStep 503 is entered, otherwise step 507 is entered, where t_sAnd loop_maxAll are preset threshold values;

step 503, get j_minFrom the vectorThe light source vector with the size of (W-1) × 1 is obtained by deletingWill j_minCorresponding ICC^sOne column in the matrix is denotedWill be provided withSlave ICC^sDeleting in the matrix to obtain new ICC with size K × (W-1)^sA matrix;

step 504, calculate matrix D ═ (ICC)^sTICC^s)^-1Calculating the projection matrix P ═ I-ICC^sDICC^sTWherein I is an identity matrix;

step 505, calculating coefficients:whereinRepresenting a vectorThe maximum value of the absolute value of each element, | ·| non-woven phosphor₂Represents a two-norm;

step 506, vector light sourceThe updating is as follows:wherein sgn {. is a sign function, andsetting all the pixel values smaller than 0 to be 0, updating the cycle variable to loop +1, and returning to the step 502;

step 507, terminating the circulation and setting the current light source vectorRecord as the light source vector after regularization

The invention has the beneficial effects that:

firstly, the SO method of the invention adopts the SELSE method to optimize the light source pattern. If newly added key area and observation point data are obtained after the light source optimization is finished, the light source does not need to be re-optimized, and the current light source optimization result can be corrected by adopting an SELSE method, so that the light source optimization result considering all key areas and observation points is obtained.

Secondly, the invention adopts SELSE method, which can realize parallel processing of ICC matrix calculation and light source optimization, thereby providing a possible approach for further improving the operational efficiency of the existing SO technology.

Thirdly, the invention adopts a reverse ORLSE method to regularize the light source graph. In each cycle iteration, the pixel point with the minimum light intensity in the light source is set to be 0, the imaging error introduced by the pixel point is projected to each column of the ICC matrix corresponding to the rest light source points, and the imaging error caused by the light source point setting to be 0 is compensated as much as possible by correcting the intensities of the rest light source points. Therefore, the light source regularization method can improve or maintain the imaging quality of the photoetching system as much as possible while reducing the complexity of the light source and improving the manufacturability of the light source.

Finally, the vector imaging model is used for describing the imaging process of the photoetching system, the vector characteristic of an electromagnetic field is considered, the optimized light source graph is not only suitable for the condition of small NA, but also suitable for the condition that NA is greater than 0.6, and the requirement of the high-NA photoetching system on simulation accuracy can be met.

Drawings

FIG. 1 is a flow chart of an adaptive SO method using SELSE and reverse ORLSE in accordance with 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 two critical areas on a wafer.

Fig. 4 is an initial light source graph and a light source graph obtained by optimizing a light source by using a SELSE method for observation point data in a first key region.

FIG. 5 is an aerial image generated at a first critical area when illuminated with the light sources of FIG. 4.

Fig. 6 is a light source graph obtained by further updating and optimizing the light source in the graph 404 by using the SELSE method with respect to the observation point data in the second key region.

FIG. 7 is an aerial image generated at first and second critical areas when illuminated with the light sources of FIG. 6.

FIG. 8 is a comparison graph of process windows of a lithography system corresponding to two critical regions before and after a light source is optimized by the SELSE method of the present invention.

Fig. 9 shows a light source pattern before light source regularization and a light source pattern after different cycle numbers are regularized by using a reverse ORLSE method.

FIG. 10 is an aerial image generated at a first critical area when illuminated with the light sources of FIG. 9.

FIG. 11 is an aerial image generated at a second critical area when illuminated with the light sources of FIG. 9.

FIG. 12 is a comparison graph of the process windows of the lithography system corresponding to two critical regions before and after the light source is regularized by the inverse ORLSE method of the present invention.

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 actual photoetching system comprises process variation factors such as defocusing and exposure variation. The stability of the lithography system to defocus and exposure variation can be evaluated using a process window. The horizontal axis of the process window is the depth of focus (DOF for short), 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 margin (EL for short), which indicates the acceptable exposure variation range under the premise of acceptable imaging quality; EL is generally expressed as the amount of change in exposure as a percentage of the rated 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 corresponding to the photoetching system is larger, the stability of the system to defocusing and exposure variation is higher. In order to expand the process window of the lithography system, the invention adopts a linear signal estimation model to construct the SO problem, namely:

${\stackrel{\&RightArrow;}{Z}}^s=\mathrm{ICC}\stackrel{\&RightArrow;}{J}+\stackrel{\&RightArrow;}{n},$

whereinForming a vector with the size of K × 1 by pixel values corresponding to all observation points on the target graph, wherein K is the number of the observation points;is a light source vector; ICC is an ICC matrix corresponding to all observation points, and the elements of the ith row and the jth column of the ICC represent light source vectorsWhen the light source at the jth point is used for illumination, the intensity of an aerial image generated at the ith observation point is controlled;is a noise vector with the size of K × 1 and is used for characterizationAndan error between canEach element in (a) is treated as having a variance σ²Is determined. By adopting the signal estimation model, the space image corresponding to the optimized light source can be as close as possible to all observation points at the waferAnd (4) target graphics. 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. Therefore, constructing the SO problem as the signal estimation problem described above can effectively extend the process window of the lithography system.

On the other hand, by adopting the SO method in the invention, if newly added key areas and observation point data are obtained after the light source optimization is finished, the light source does not need to be re-optimized, and only the SELSE method needs to be adopted to correct the current light source optimization result, SO that the light source optimization result considering all the key areas and the observation points is obtained. Meanwhile, the invention adopts SELSE method, which can realize parallel processing of ICC matrix calculation and light source optimization, thereby providing a possible approach for further improving the operational efficiency of the existing SO technology.

Meanwhile, after obtaining a light source optimization result, the SO method in the invention adopts a reverse ORLSE method to regularize the light source, in each cycle iteration, the pixel point with the minimum light intensity in the light source is set to be 0, the introduced imaging error is projected to each column of an ICC matrix corresponding to the other light source points, and the imaging error caused by the light source point setting to be 0 is compensated as much as possible by correcting the intensities of the other light source points. Therefore, the method of the invention is adopted to regularize the light source, and the imaging quality of the photoetching system can be improved or kept as much as possible while the complexity of the light source is reduced and the manufacturability of the light source is improved.

As shown in fig. 1, the self-adaptive SO method using SELSE and reverse ORLSE of the present invention specifically includes the steps of:

step 101, initializing a light source to a size of N_S×N_SLight source pattern J, mask pattern M and target patternGraph rasterized to N × N, initializing sizeIs N_S ²×N_S ²The SELSE covariance matrix sigma, initializing the variance σ of the noise vector²Initializing ICC matrix to be a null matrix, recording as ICC, and vectorInitialized to a null vector, where N_SAnd N is an integer.

102, scanning the light source graph J line by line from top left to bottom right, and converting the J into N_S ²× 1 light source vectorIs the pixel value of the light source pattern J.

Step 103, calculating each light source pixel point (x)_s,y_s) Corresponding x-axis component equivalent point spread functiony-axis component equivalent point spread functionAnd z-axis component equivalent point spread function

Step 103 of the present invention calculates a light source pixel (x)_s,y_s) Corresponding equivalent point spread function Andthe method comprises the following specific steps:

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 by 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 (α)_s,β_s,γ_s) Then the relationship between the global coordinate and the direction cosine is:

${\mathrm{\&alpha;}}_s=x_s\&CenterDot;{\mathrm{NA}}_m,{\mathrm{\&beta;}}_s=y_s\&CenterDot;{\mathrm{NA}}_m,{\mathrm{\&gamma;}}_s=\cos \left[{\sin }^{-1}({\mathrm{NA}}_m\&CenterDot;\sqrt{x_s^2+y_s^2})\right],$

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 cosine of the direction 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_||)，e_⊥The axis being the direction of vibration of the TE-polarized light in the light emitted by the light source, e_||The axis is the vibration direction of the TM polarized light in the light emitted by the light source. Wave vector ofThe 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:

$\left[\begin{array}{c}{E}_x\\ E_y\\ E_z\end{array}\right]=T\&CenterDot;\left[\begin{array}{c}{E}_{\&perp;}\\ E_{\left|\right|}\end{array}\right],$

wherein E is_x、E_yAnd E_zRespectively the component of the electric field of the light wave emitted by the light source in the global coordinate system, E_⊥And E_||The component of the electric field of the light wave emitted by the light source in the local coordinate system, and the transformation matrix T is:

$T=\left[\begin{array}{cc}-\frac{\mathrm{\&beta;}}{\mathrm{\&rho;}}& -\frac{\mathrm{\&alpha;\&gamma;}}{\mathrm{\&rho;}}\\ \frac{\mathrm{\&alpha;}}{\mathrm{\&rho;}}& -\frac{\mathrm{\&beta;\&gamma;}}{\mathrm{\&rho;}}\\ 0& \mathrm{\&rho;}\end{array}\right],$

wherein, $\mathrm{\&rho;}=\sqrt{{\mathrm{\&alpha;}}^2+{\mathrm{\&beta;}}^2}.$

calculating an equivalent point spread functionAndthe method comprises the following specific steps:

step 201, aiming at a single point light source (x)_s,y_s) Calculating the vector matrix of N × NEach element being equal toRepresenting a point source (x)_s,y_s) The electric field vector of the electric field of the emitted light wave in the global coordinate system. If point light source (x) is set_s,y_s) The electric field that emits the light wave is represented in the local coordinate system as:

${\stackrel{\&RightArrow;}{E}}_i^{x_s,y_s}=\left[\begin{array}{c}{E}_{\&perp;}\\ E_{\left|\right|}\end{array}\right],$

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

${\stackrel{\&RightArrow;}{E}}_i^{x_s{y_s}^{\&prime;}}=T\&CenterDot;{\stackrel{\&RightArrow;}{E}}_i^{x_s{y}_s}.$

step 202, for a single point light source (x)_s,y_s) Calculating the electric field vector rotation matrix from the front of the exit pupil to the back of the exit pupilWhereinIs a vector matrix of size N × N, each element being a matrix of 3 × 3, which can be calculated from (α ', β', γ) (. sup.). sup.Andα ', β', sin phi ', sin theta', gamma ', cos theta', the direction cosine (wave vector) of the plane wave incident on the image plane from the exit pupil of the projection system isPhi 'and theta' are the azimuth and elevation angles, respectively, of the wave vectorAndthe relation of (A) is as follows:

wherein,is a vector matrix of N × N, each element being a matrix of 3 × 3:

$V(m,n)=\left[\begin{array}{ccc}\frac{{\mathrm{\&beta;}}^{\&prime;2}+{\mathrm{\&alpha;}}^{\&prime;2}{\mathrm{\&gamma;}}^{\&prime;}}{1-{\mathrm{\&gamma;}}^{\&prime;2}}& -\frac{{\mathrm{\&alpha;}}^{\&prime;}{\mathrm{\&beta;}}^{\&prime;}}{1+{\mathrm{\&gamma;}}^{\&prime;}}& {\mathrm{\&alpha;}}^{\&prime;}\\ -\frac{{\mathrm{\&alpha;}}^{\&prime;}{\mathrm{\&beta;}}^{\&prime;}}{1+{\mathrm{\&gamma;}}^{\&prime;}}& \frac{{\mathrm{\&alpha;}}^{\&prime;2}+{\mathrm{\&beta;}}^{\&prime;2}{\mathrm{\&gamma;}}^{\&prime;}}{1-{\mathrm{\&gamma;}}^{\&prime;2}}& {\mathrm{\&beta;}}^{\&prime;}\\ -{\mathrm{\&alpha;}}^{\&prime;}& -{\mathrm{\&beta;}}^{\&prime;}& {\mathrm{\&gamma;}}^{\&prime;}\end{array}\right]$ m,n＝1,2,...,N。

step 203, aiming at a single point light source (x)_s,y_s) Calculating the vector matrix of N × NA scalar matrix representing the finite acceptance of the diffraction spectrum by the numerical aperture of the projection system, i.e. a value of 1 inside the pupil and a value of 0 outside the pupil, is specified as follows:

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

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

Step 204, respectively extractingX-direction component of each element inComponent in y directionAnd the z-direction componentObtaining three scalar matrices of size N × NAnd

step 205, byAndcalculating light source pixel (x)_s,y_s) Corresponding equivalent point spread functionAndp ═ x, y, z, where n_mR is the reduction ratio of an ideal projection system, and is generally 4, F^-1Is an inverse Fourier transform.

Step 104, selecting a new observation point in a critical area on the waferSelecting vectorsMiddle corresponding observation pointElement z of^s(ii) a Calculating corresponding observation pointsNew row of the ICC matrixIts size is 1 × N_S ²Wherein T is a transpose operation; will be provided withSupplementing the current ICC matrix as the lowest row; will z^sAs a last element to supplement the currentIn the vector.

Step 104 of the present invention calculates the corresponding observation pointsNew row of the ICC matrixThe method comprises the following specific steps:

step 301, rasterizing a light source pattern J into N_S×N_SAnd each pixel is used as a point light source.

Step 302, for a single point light source (x)_s,y_s) Obtaining observation points on the corresponding wafer when the point light source is illuminatedIntensity of aerial image ofFirst calculate the point light source (x)_s,y_s) Corresponding to observation points on the wafer during illuminationX, y, and z-directional components of the electric field intensity of (1):

$E_p^{\mathrm{wafer}}(x_s,y_s,{\tilde{x}}_w,{\tilde{y}}_w)={\mathrm{\&Sigma;}}_{x_w}{\mathrm{\&Sigma;}}_{y_w}{H}_p(x_w,y_w)\&times;[B({\tilde{x}}_w-x_w,{\tilde{y}}_w-y_w)\&times;M({\tilde{x}}_w-x_w,{\tilde{y}}_w-y_w)],$ p＝x,y,z

where M is a mask pattern of size NxN, B is a scalar matrix of size NxN, called the diffraction matrix of the mask, and each element in B is a scalar, and according to the Hopkins (Hopkins) approximation, each element of B can be represented as:

$\begin{array}{c}B(m,n)=\exp \left(\frac{j2\mathrm{\&pi;}{\mathrm{\&beta;}}_{s}x}{\mathrm{\&lambda;}}\right)\exp \left(\frac{j2\mathrm{\&pi;}{\mathrm{\&alpha;}}_{s}y}{\mathrm{\&lambda;}}\right)\\ =\exp \left(\frac{j2\mathrm{\&pi;m}{y}_s{\mathrm{NA}}_m\&times;\mathrm{pixel}}{\mathrm{\&lambda;}}\right)\exp \left(\frac{j2\mathrm{\&pi;}{\mathrm{nx}}_s{\mathrm{NA}}_m\&times;\mathrm{pixel}}{\mathrm{\&lambda;}}\right),\end{array}$ m，n＝1，2，...，N

in the above formula, pixel represents the side length of a single pixel on the mask pattern. Corresponding to the observation point on the waferThe aerial image intensity of (a) can be expressed as:

step 303, determining whether all the point light sources have been calculated, corresponding to the observation pointsIf yes, go to step 304, otherwise go back to step 302.

Step 304, scanning the light source graph J line by line from top left to bottom right, and illuminating all the point light sources according to the scanning sequence, wherein the observation points correspond to the point light sourcesIs arranged to have a size of 1 × N_S ²Vector of (2)And takes it as the corresponding observation pointA new row of the ICC matrix.

Step 105, updating the light source vector by adopting SELSE method

In step 105, the invention updates the light source vector by using a SELSE methodThe specific process comprises the following steps:

step 401, calculateSize N_S ²× 1 gain factorThe current SELSE covariance matrix is recorded as Σ [ n-1 ]]Update Σ toWhere I is the identity matrix.

Step 402, recording the current light source vector asThe light source vector is updated as:

step 403, calculating a light source vectorAnd is noted as the minimum element value of

Step 404, update σ as:whereinRepresenting light source vectorThe minimum element value in (c), ω > 1, is a predetermined magnification factor.

Step 405, ifStep 106 is entered, otherwise step 406 is entered.

Step (ii) of406. Calculated size N_S ²× 1 gain factorUpdate sigma toWhere I is the identity matrix.

Step 407, updating the light source vector to:and will beAll the pixel values smaller than 0 are set to 0.

Step 106, if there are new observation points on the wafer, returning to step 104; otherwise step 107 is entered.

Step 107, calculating the regularized light source vector by adopting a reverse ORLSE method

In step 107, the invention adopts a reverse ORLSE method to calculate the regularized light source vectorThe specific process comprises the following steps:

step 501, assuming that the total number of currently selected observation points is K, the size of the current ICC matrix is K × N_S ²Current vectorSize of K × 1, from size N_S ²× 1 light source vectorFind all elements with value equal to 0, and apply these elementsFromDeleting to obtain new light source vector with W × 1 sizeDeleting the columns in the ICC matrix corresponding to the elements from the ICC matrix to obtain a new ICC matrix with the size of K × W, which is recorded as ICC^sWherein W is the light source vectorThe number of all elements greater than 0; the loop number variable is set to 0.

Step 502, determining a light source vectorElement j having the minimum value of_minIf j is_min<t_sAnd loop < loop_maxStep 503 is entered, otherwise step 507 is entered, where t_sAnd loop_maxAre all preset threshold values.

Step 503, get j_minFrom the vectorThe light source vector with the size of (W-1) × 1 is obtained by deletingWill j_minCorresponding ICC^sOne column in the matrix is denotedWill be provided withSlave ICC^sDeleting in the matrix to obtain new ICC with size K × (W-1)^sAnd (4) matrix.

Step 504, calculate matrix D ═ (ICC)^sTICC^s)^-1Calculating the projection matrix P ═ I-ICC^sDICC^sTWherein I is an identity matrix.

Step 505, calculating coefficients:whereinRepresenting a vectorThe maximum value of the absolute value of each element, | ·| non-woven phosphor₂Representing a two-norm.

Step 506, vector light sourceThe updating is as follows:wherein sgn {. is a sign function, andall the pixel values smaller than 0 are set to be 0, the loop number variable is updated to loop +1, and the process returns to step 502.

Step 507, terminating the circulation and setting the current light source vectorRecord as the light source vector after regularization

Example of implementation of the invention:

fig. 3 is a schematic diagram of two critical areas on a wafer, which are also target patterns, white for open areas and black for light-blocking areas, and the critical dimension of which is 45 nm. Where the lines in the critical area shown at 301 are in the vertical direction and the lines in the critical area shown at 302 are in the horizontal direction.

Fig. 4 is an initial light source graph and a light source graph obtained by optimizing a light source by using a SELSE method for observation point data in a first key region. The initial light source shown at 401 is a ring light source; 402 is a result obtained by optimizing the light source by using a SELSE method for 2 observation point data in the first key area; 403 is a result obtained by optimizing the light source by using a SELSE method for 7 observation point data in the first key region; 404 is a result of optimizing the light source by using the SELSE method for 100 observation point data in the first critical area.

FIG. 5 is an aerial image generated at a first critical area when illuminated with the light sources of FIG. 4. 501 is an aerial image generated at a first key area when the light source shown in 401 is adopted for illumination; 502 is the aerial image produced at the first critical area when illuminated with the light source shown at 402; 503 is the aerial image generated at the first critical area when illuminated with the light source shown in 403; 504 is the aerial image produced at the first critical area when illuminated with the light source shown at 404.

Fig. 6 is a light source graph obtained by further updating and optimizing the light source in the graph 404 by using the SELSE method with respect to the observation point data in the second key region. 601 is a result of further updating and optimizing the light source in 404 by adopting a SELSE method aiming at 1 observation point data on the second key area; 602 is a result obtained by further updating and optimizing the light source in 404 by adopting a SELSE method for 50 observation point data in the second key area; 603 is a result obtained by further updating and optimizing the light source in 404 by adopting a SELSE method aiming at the data of 90 observation points in the second key area; 604 is the result of further updating and optimizing the light source in 404 by using the SELSE method for 100 observation point data in the second critical area.

FIG. 7 is an aerial image generated at first and second critical areas when illuminated with the light sources of FIG. 6. 701 is an aerial image generated at the first key region when the light source shown in 601 is adopted for illumination; 702 is the aerial image generated at the second critical area when illuminated with the light source shown at 601; 703 is the aerial image generated at the first critical area when the light source shown in 602 is used for illumination; 704 is the aerial image generated at the second critical area when illuminated with the light source shown at 602; 705 is the aerial image produced at the first critical area when illuminated with the light source of 603; 706 is the aerial image produced at the second critical area when illuminated with the light source shown at 603; 707, the aerial image generated at the first critical area when illuminated with the light source shown in 604; 708 is the aerial image produced at the second critical area when illuminated with the light source shown at 604.

FIG. 8 is a comparison graph of process windows of a lithography system corresponding to two critical regions before and after a light source is optimized by the SELSE method of the present invention. 801 is a process window corresponding to a first key area when an initial light source before optimization is adopted for illumination; 802 is a process window corresponding to a first key area after a light source is optimized by adopting the SELSE method in the invention; 803 is a process window corresponding to the second key area when the initial light source before optimization is used for illumination; and 804 is a process window corresponding to the second critical area after the light source is optimized by the SELSE method in the invention.

Fig. 9 shows a light source pattern before light source regularization and a light source pattern after different cycle numbers are regularized by using a reverse ORLSE method. 901 is the initial light source pattern before regularization, which is consistent with the light source shown in 604; 902 is a light source pattern obtained after 30 regularization cycles; 903 is a light source pattern obtained after 40 regularization cycles; 904 is the light source pattern obtained after 51 regularization cycles.

FIG. 10 is an aerial image generated at a first critical area when illuminated with the light sources of FIG. 9. 1001 is a space image generated at a first key area when the light source shown in 901 is adopted for illumination; 1002 is the aerial image generated at the first critical area when illuminated with the light source shown at 902; 1003 is an aerial image generated at the first critical area when the light source 903 is adopted for illumination; 1004 is the aerial image produced at the first critical area when illuminated with the light source shown at 904.

FIG. 11 is an aerial image generated at a second critical area when illuminated with the light sources of FIG. 9. 1101 is the aerial image generated at the second critical area when the light source shown by 901 is used for illumination; 1102 is the aerial image produced at the second critical area when illuminated with the light source shown at 902; 1103 is the aerial image generated at the second critical area when illuminated with the light source shown at 903; 1104 is the aerial image produced at the second critical area when illuminated with the light source shown at 904.

FIG. 12 is a comparison graph of the process windows of the lithography system corresponding to two critical regions before and after the light source is regularized by the inverse ORLSE method of the present invention. 1201 is a process window corresponding to the first key area when the light source which is not regulated in 901 is used for illumination; 1202 is a process window corresponding to a first key area after the light source in 901 is regularized by using an ORLSE method in the present invention; 1203 is a process window corresponding to the second key area when the light source which is not regulated in 901 is used for lighting; 1204 is a process window corresponding to the second key region after the light source in 901 is regularized by the ORLSE method of the present invention.

Comparing fig. 4-12, the SO process of the present invention has the following effects: firstly, the SO method in the invention can effectively improve the process windows of the photoetching system at different key areas. Secondly, after the light source is optimized by adopting the SO method in the invention, if newly added key regions and observation point data are obtained, the light source does not need to be re-optimized, but the current light source optimization result can be corrected by adopting the SELSE method, SO that the light source optimization result considering all the key regions and the observation points is obtained. Thirdly, by adopting the SO method in the invention, the parallel processing of ICC matrix calculation and light source optimization can be realized. Fourthly, the light source regularization method can improve or keep the imaging quality of the photoetching system as much as possible while reducing the complexity of the light source and improving the manufacturability of the light source, and effectively expand the process windows of the photoetching system in different key areas. Fifthly, the imaging process of the photoetching system is described by using the vector imaging model, the optimized light source graph is not only suitable for the condition of small NA, but also suitable for the condition that NA is greater than 0.6, and the simulation requirement of the photoetching system with high NA can be met.

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 (5)

1. A self-adaptive photoetching system light source optimization method is characterized by comprising the following specific steps:

step 101, initializing a light source to a size of N_S×N_SLight source pattern J, mask pattern M and target patternGraph rasterized to N × N, initialized with size N_S ²×N_S ²Sequential least squares estimation (sequentiallestqualeestimato)r, SELSE for short) covariance matrix Σ, variance σ of the initialized noise vector²Initializing the illumination cross coefficient matrix to a null matrix, denoted as ICC, and vectorInitialized to a null vector, where N_SAnd N is an integer;

102, scanning the light source graph J line by line from top left to bottom right, and converting the J into N_S ²× 1 light source vectorThe element value of (b) is a pixel value of the light source pattern J;

step 103, calculating each light source pixel point (x)_s,y_s) Corresponding x-axis component equivalent point spread functiony-axis component equivalent point spread functionAnd z-axis component equivalent point spread function

Step 104, selecting a new observation point in a critical area on the waferSelecting vectorsMiddle corresponding observation pointElement z of^s(ii) a Calculating corresponding observation pointsNew row of the ICC matrixIts size is 1 × N_S ²Wherein T is a transpose operation; will be provided withSupplementing the current ICC matrix as the lowest row; will z^sAs a last element to supplement the currentVector is carried out;

step 105, updating the light source vector by adopting SELSE method

Step 106, if there are new observation points on the wafer, returning to step 104; otherwise, go to step 107;

step 107, calculating the regularized light source vector by using a reverse Order Recursive Least Square Estimation (ORLSE) method

Step 108, the light source vector after the regularization is carried outPerforming a reverse scan operation onEach element value in (1) is assigned to a corresponding N_S×N_SAnd setting other pixels on the light source pattern to 0, and recording the obtained light source pattern asNamely the optimized light source pattern.

2. The adaptive light source optimization method for lithography system according to claim 1, wherein said step 103 comprises calculating light source pixel points (x)_s,y_s) Corresponding equivalent point spread functionAndthe method comprises the following specific steps:

setting the direction of the optical axis as the z-axis, and establishing a global coordinate system according to the principle of the left-hand coordinate system, (α, gamma) is the coordinate system after Fourier transformation of the global coordinate system (x, y, z) on the mask, (α ', β ', gamma ') is the global coordinate system (x) on the wafer_w,y_w,z_w) A coordinate system after Fourier transform;

step 201, aiming at a single point light source (x)_s,y_s) Calculating the vector matrix of N × N(if all elements of a matrix are matrices or vectors, it is called a vector matrix), each element being equal toRepresenting a point source (x)_s,y_s) An electric field vector of an electric field emitting the light wave in a global coordinate system;

step 202, for a single point light source (x)_s,y_s) Calculating the electric field vector rotation matrix from the front of the exit pupil to the back of the exit pupilWhereinIs a vector matrix of size N × N, each element being a matrix of 3 × 3, which can be calculated from (α ', β ', γ ');

step 203, aiming at a single point light source (x)_s,y_s) Calculating the vector matrix of N × NWhere U is the pupil filtering function and,is a vector of 3 × 1 for each element ofm,n＝1,...N；

Step 204, respectively extractingX-direction component of each element inComponent in y directionAnd the z-direction componentObtaining three scalar matrices of size N × NAnd

step 205, byAndcalculating light source pixel (x)_s,y_s) Corresponding equivalent point spread functionAnd

3. the adaptive photolithography system light source optimization method according to claim 1 or 2, wherein the step 104 of calculating the observation points corresponding to the observation pointsNew row of the ICC matrixThe method comprises the following specific steps:

step 301, rasterizing a light source pattern J into N_S×N_SA plurality of pixels, each pixel serving as a point light source;

step 302, for a single point light source (x)_s,y_s) Obtaining observation points on the corresponding wafer when the point light source is illuminatedIntensity of aerial image of

Step 303, determining whether all the point light sources have been calculated, corresponding to the observation pointsIf yes, go to step 304, otherwise go back to step 302;

step 304, scanning the light source graph J line by line from top left to bottom right, and illuminating all the point light sources according to the scanning sequence, wherein the observation points correspond to the point light sourcesIs arranged to have a size of 1 × N_S ²Vector of (2)And takes it as the corresponding observation pointA new row of the ICC matrix.

4. The method of claim 1 or 2, wherein the step 105 is performed by a SELSE method to update the light source vectorThe specific process comprises the following steps:

step 401, calculate the size N_S ²× 1 gain factorThe current SELSE covariance matrix is recorded as Σ [ n-1 ]]Update Σ toWherein I is an identity matrix;

step 402, recording the current light source vector asThe light source vector is updated as:

step 403, calculating a light source vectorAnd is noted as the minimum element value of

Step 404, update σ as:whereinRepresenting light source vectorThe minimum element value in (c), omega > 1 is a preset amplification factor;

step 405, ifStep 106 is entered, otherwise step 406 is entered;

step 406, calculate the size N_S ²× 1 gain factorUpdate sigma toWherein I is an identity matrix;

step 407, updating the light source vector to:and will beAll the pixel values smaller than 0 are set to 0.

5. The adaptive light source optimization method for lithography system according to claim 1 or 2, wherein the step 107 employs inverse ORLSE method to calculate the regularized light source vectorThe specific process comprises the following steps:

step 501, assuming that the total number of currently selected observation points is K, the size of the current ICC matrix is K × N_S ²Current vectorSize of K × 1, from size N_S ²× 1 light source vectorFinds all elements with value equal to 0, and removes these elements fromDeleting to obtain new light source vector with W × 1 sizeDeleting the columns in the ICC matrix corresponding to the elements from the ICC matrix to obtain a new ICC matrix with the size of K × W, which is recorded as ICC^sWherein W is the light source vectorThe number of all elements greater than 0; setting the loop variable to be 0;

step 502, determining a light source vectorElement j having the minimum value of_minIf j is_min<t_sAnd loop < loop_maxThen, thenStep 503 is entered, otherwise step 507 is entered, where t_sAnd loop_maxAll are preset threshold values;

step 503, get j_minFrom the vectorThe light source vector with the size of (W-1) × 1 is obtained by deletingWill j_minCorresponding ICC^sOne column in the matrix is denotedWill be provided withSlave ICC^sDeleting in the matrix to obtain new ICC with size K × (W-1)^sA matrix;

step 504, calculate matrix D ═ (ICC)^sTICC^s)^-1Calculating the projection matrix P ═ I-ICC^sDICC^sTWherein I is an identity matrix;

step 505, calculating coefficients:whereinRepresenting a vectorThe maximum value of the absolute value of each element, | ·| non-woven phosphor₂Represents a two-norm;

step 506, vector light sourceThe updating is as follows:wherein sgn {. is a sign function, andsetting all the pixel values smaller than 0 to be 0, updating the cycle variable to loop +1, and returning to the step 502;

step 507, terminating the circulation and setting the current light source vectorRecord as the light source vector after regularization