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

A kind of adaptive optical etching system light source optimization method

Technical field

The present invention relates to a kind of recursive least square that adopts and estimate (sequentialleastsquareestimator, be called for short SELSE) and reverse rank recurrence least square estimation (order-recursiveleastsquareestimator, be called for short ORLSE) adaptive optical etching system light source optimization method, belong to photoetching resolution strengthen technical field.

Background technology

Current great scale integrated circuit mainly adopts the ArF deep UV (ultraviolet light) etching system of 193nm to manufacture, along with integrated circuit critical size (criticaldimension, be called for short CD) continuous reduction and the improving constantly of integrated level, resolution enhance technology (resolutionenhancementtechnique is called for short RET) must be adopted to improve imaging resolution and the anti-aliasing degree of etching system.Light source is optimized, and (sourceoptimization is called for short SO) is a kind of important photoetching resolution enhancing technology.SO technology, by optimizing the light distribution of light source, is modulated the light intensity of the light of incident mask and direction, thus is improved the imaging performance in full die circuit features corresponding to each critical area (hotspot).Wherein, critical area refers in certain processing variation range, is difficult to as the region of plane being possessed higher anti-aliasing degree.A large amount of critical areas with different geometric properties generally can be comprised in full die circuit features.But, along with constantly reducing of integrated circuit critical size, the continuous rising of integrated level and overall dimensions, and the introducing of vector imaging model with higher simulation accuracy, existing SO technology faces data processing amount and computation complexity significantly increases, and the problem that operation efficiency is lower.On the other hand, recent related researcher adopts free form diffractive optical element (freeformdiffractionopticalelements is called for short DOE) and micro reflector array, achieves the SO technology of pixelation.Compare traditional parametrization SO technology, pixelation SO technology greatly improves light source and optimizes degree of freedom, thus can the imaging performance of more efficiently raising etching system.But the light source optimum results adopting pixelation SO technology to obtain often has higher complexity, thus reduces the manufacturability of light source.Therefore, how to reduce optimize after light source complexity, improve the manufacturability of light source and become one of major issue in pixelation SO technology.

Pertinent literature (OpticsExpress, 2014,22 (12): 14180-14198) adopts compressed sensing (compressivesensing is called for short CS) technology to propose a kind of higher SO method of operation efficiency.The method demarcates some observation stations at wafer place, is optimized and the imaging at these observation station places is tried one's best close to targeted graphical, thus improve the image quality in whole image planes by SO.The etching system aerial image model that the method adopts is: wherein for the vector that the aerial image light intensity value at pixel places all on wafer forms, for the vector obtained after lining by line scan to light source figure, be called light source vector, ICC is illumination interaction coefficent (illuminationcrosscoefficient is called for short ICC) matrix.The method needs first to calculate complete ICC matrix, afterwards according to above-mentioned imaging model, is optimized light source.Therefore, said method has the deficiency of following two aspects: the first, before light source is optimized, the method must detect all critical areas in full die circuit features, and selectes observation station for all critical areas, calculates the complete ICC matrix corresponding to all observation stations afterwards.After light source optimization terminates, once new critical area and observation station be detected, original light source optimum results will be no longer optimal result for newly-increased critical area and observation station.Therefore, we must expand original ICC matrix, make it comprise newly-increased critical area and the data of observation station, are then again optimized light source.Therefore, newly-increased critical area and the points of measurement are according to causing a large amount of repeated optimization calculated amount.The second, the computation complexity of ICC matrix is higher, consuming time longer, and the method must calculate complete ICC matrix before light source is optimized, thus parallel computation mode cannot be used simultaneously to carry out the calculating of ICC matrix and the optimization of light source, thus limit the further lifting of this algorithm operation efficiency.In sum, existing SO method cannot according to newly-increased critical area and observation station, the existing light source optimum results of adaptive renewal, cannot realize the parallel processing of ICC matrix computations and light source optimization simultaneously, be further improved.

On the other hand, pertinent literature (AppliedOptics, 2013,52 (18): 4200-4211) proposes a kind of rule method for reducing light source optimum results complexity.The method is after light source optimization terminates, and the light source pixel point first all light intensity being less than predetermined threshold sets to 0.Afterwards, all light source pixel of searching loop, for each light source pixel, if non-zero pixels number is less than 3 in be adjacent 8 light source pixel, then set to 0 this light source pixel point.But the method, while reduction light source figure complexity, does not consider that light source simplifies the impact on etching system imaging performance.Therefore, existing light source rule method, while reduction light source complexity, is difficult to the image quality improving or keep etching system, is further improved.

Summary of the invention

The object of this invention is to provide a kind of adaptive optical etching system light source optimization method adopting SELSE and reverse ORLSE, SO optimization problem is converted into signal estimation problems by the method, thus reaches the object of regularization light source figure, reduction light source complexity.Realize technical scheme of the present invention as follows:

A kind of adaptive optical etching system light source optimization method, concrete steps are:

Step 101, light source is initialized as size is N _s× N _slight source figure J, by mask graph M and targeted graphical grid turns to the figure of N × N, and initialization size is N _s ²× N _s ²sELSE covariance matrix Σ, the variances sigma of initialization noise vector ², be an empty matrix by ICC matrix initialisation, be designated as ICC, by vector be initialized as blank vector, wherein a N _sbe integer with N;

Step 102, lining by line scan from upper left to bottom right is carried out to light source figure J, and J is converted into N _s ²the light source vector of × 1 element value be the pixel value of light source figure J;

Step 103, calculate each light source pixel point (x _s, y _s) corresponding x-axis component equivalent point spread function y-axis component equivalent point spread function with z-axis component equivalent point spread function

The observation station that one new is selected in step 104, critical area on wafer choose vector middle corresponding observation station element z ^s; Calculate and correspond to observation station new a line of ICC matrix its size is 1 × N _s ², wherein T is matrix transpose operation; Will a line as bottom adds in current ICC matrix; By z ^sadd to current as last element in vector;

Step 105, employing SELSE method, more new light sources vector

If step 106 has newly-increased observation station on wafer, then return step 104; Otherwise enter step 107;

Step 107, adopt reverse ORLSE method, the light source vector after computation rule

Step 108, to after regularization light source vector carry out retrograde scan operation, will in each element value be assigned to corresponding N _s× N _sthe pixel of light source figure, and other pixels on light source figure to be set to 0, obtained light source figure are designated as be the light source figure after optimization.

Step 103 of the present invention calculates light source pixel point (x _s, y _s) corresponding equivalent point spread function with concrete steps be:

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

Step 201, for a single point light source (x _s, y _s), calculate the vector matrix of N × N each element is equal to representative point light source (x _s, y _s) send the electric field intensity of electric field in global coordinate system of light wave;

Step 202, for a single point light source (x _s, y _s), calculate the electric field intensity rotation matrix from emergent pupil front to emergent pupil rear wherein be a size be the vector matrix of N × N, each element is the matrix of 3 × 3, can be calculated by (α ', β ', γ ');

Step 203, for a single point light source (x _s, y _s), calculate the vector matrix of N × N wherein U is pupil filtering function, each element be the vector of 3 × 1 m, n=1 ... N;

Step 204, to extract respectively in the x durection component of each element y durection component with z durection component obtaining three sizes is the scalar matrix of N × N with

Step 205, by with calculate light source pixel point (x _s, y _s) corresponding equivalent point spread function with

Step 104 of the present invention calculates and corresponds to observation station new a line of ICC matrix concrete steps be:

Step 301, light source figure J grid is turned to N _s× N _sindividual pixel, each pixel is as a pointolite;

Step 302, for a single point light source (x _s, y _s), observation station on corresponding wafer when obtaining this spot light aerial image intensity

Step 303, when judging whether to calculate all spot lights, corresponding to observation station aerial image intensity, if so, then enter step 304, otherwise return step 302;

Step 304, lining by line scan of upper left to bottom right is carried out to light source figure J, and according to scanning sequency by all spot lights time, corresponding to observation station aerial image intensity to be arranged as a size be 1 × N _s ²vector and it can be used as corresponding to observation station new a line of ICC matrix.

SELSE method is adopted, more new light sources vector in step 105 of the present invention detailed process be:

Step 401, calculating size are N _s ²the gain factor of × 1 current SELSE covariance matrix is designated as Σ [n-1], Σ is updated to wherein I is unit matrix;

Step 402, current light source vector to be designated as light source vector is updated to:

Step 403, calculating light source vector in least member value, and to be designated as

Step 404, σ to be updated to: wherein represent light source vector in least member value, the amplification factor of ω > 1 for presetting;

If step 405 then enter step 106, otherwise enter step 406;

Step 406, calculating size are N _s ²the gain factor of × 1 Σ is updated to wherein I is unit matrix;

Step 407, light source vector to be updated to: and will in all pixel values being less than 0 be set to 0.

Reverse ORLSE method is adopted, the light source vector after computation rule in step 107 of the present invention detailed process be:

Step 501, suppose that the observation station of current selection adds up to K, then the size of current ICC matrix is K × N _s ², current vector size be K × 1; Be N from size _s ²the light source vector of × 1 in find all values to equal the element of 0, by these elements from middle deletion, obtains the light source vector that new size is W × 1 row in ICC matrix corresponding to these elements are deleted from ICC matrix, obtains the ICC matrix that new size is K × W, be designated as ICC ^s, wherein W is light source vector in all numbers being greater than the element of 0; Cycle index variable is set to loop=0;

Step 502, determine light source vector in there is the element j of minimum value _minif, j _min<t _sand loop < loop _max, then enter step 503, otherwise enter step 507, wherein t _sand loop _maxbe the threshold value preset;

Step 503, by j _minfrom vector middle deletion, obtains the light source vector that size is (W-1) × 1 by j _mincorresponding ICC ^srow in matrix are designated as will from ICC ^sdelete in matrix, obtain the ICC that new size is K × (W-1) ^smatrix;

Step 504, compute matrix D=(ICC ^sTiCC ^s) ^-1, calculate projection matrix P=I-ICC ^sdICC ^sT, wherein I is unit matrix;

Step 505, design factor: wherein represent vector in the maximal value of each element absolute value, || || ₂represent two norms;

Step 506, by light source vector be updated to: wherein sgn{} is sign function, by obtained in all pixel values being less than 0 be set to 0, be loop+1 by cycle index variable update, and return step 502;

Step 507, termination circulation, and by current light source vector be designated as the vector of the light source after regularization

Beneficial effect of the present invention:

The first, the SO method that the present invention relates to adopts SELSE method to be optimized light source figure.If obtain newly-increased critical area and the points of measurement certificate after light source optimization terminates, then without the need to again optimizing light source, and SELSE method can be adopted to revise current light source optimum results, thus obtain the light source optimum results considering whole critical area and observation station.

The second, the present invention adopts SELSE method, can realize the parallel processing of ICC matrix computations and light source optimization, thus is that the operation efficiency improving existing SO technology further provides possible approaches.

3rd, the present invention adopts reverse ORLSE method to carry out regularization to light source figure.In each loop iteration, pixel minimum for light intensity in light source is set to 0, and the image error introduced thus is projected on each row of the ICC matrix corresponding to all the other light source points, by revising the intensity of all the other light source points, compensating as far as possible and setting to 0 by above-mentioned light source point the image error caused.Therefore, the light source rule method in the present invention while reduction light source complexity, raising light source manufacturability, can improve as far as possible or keep the image quality of etching system.

Finally, the present invention utilizes vector imaging model to describe the imaging process of etching system, consider the vectorial property of electromagnetic field, light source figure after optimization is not only applicable to the situation of little NA, also be applicable to the situation of NA>0.6, the simulation accuracy requirement of high NA etching system can be met.

Accompanying drawing explanation

Fig. 1 is the process flow diagram that the present invention adopts the self-adaptation SO method of SELSE and reverse ORLSE.

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

Fig. 3 is two critical area schematic diagram on wafer.

Fig. 4 is primary light source figure, and for the points of measurement certificate on first critical area, the light source figure obtained after adopting SELSE method to be optimized light source.

Fig. 5 is the aerial image produced at first critical area place when adopting each light illumination in Fig. 4.

Fig. 6 is for the points of measurement certificate on second critical area, the light source figure obtained after adopting SELSE method to carry out upgrading optimization further to light source in Figure 40 4.

Fig. 7 is at the aerial image that first and second critical area place produce when adopting each light illumination in Fig. 6.

Fig. 8 adopts the SELSE method in the present invention to optimize front and back to light source, the etching system process window comparison diagram that two critical areas are corresponding.

Fig. 9 is the light source figure before light source regularization, and adopts reverse ORLSE method, carries out the light source figure after different cycle index regularization.

Figure 10 is the aerial image produced at first critical area place when adopting each light illumination in Fig. 9.

Figure 11 is the aerial image produced at second critical area place when adopting each light illumination in Fig. 9.

Figure 12 adopts the reverse ORLSE method in the present invention to carry out before and after regularization to light source, the etching system process window comparison diagram corresponding to two critical areas.

Embodiment

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

Principle of the present invention: actual light etching system comprises the technique change such as out of focus, variation of exposure factor.The stability of etching system to out of focus and variation of exposure can be evaluated with process window.The transverse axis of process window is depth of focus (Depthoffocus is called for short DOF), represents under the acceptable prerequisite of image quality, the maximum disparity between actual wafer position and desirable image planes.The longitudinal axis of process window is exposure allowance (Exposurelatitude is called for short EL), represents under the acceptable prerequisite of image quality, acceptable variation of exposure scope; Usually variable quantity EL being expressed as exposure accounts for the form of the number percent of nominal exposure amount.The opening of process window contains all correspondence combinations meeting DOF and the EL that particular manufacturing process requires.Above-mentioned specific manufacture process requirement generally comprises critical size (CD) error, the isoparametric requirement of the side wall angle of image profiles in photoresist.When the process window that etching system is corresponding is larger, then the stability of this system to out of focus and variation of exposure is higher.In order to expand the process window of etching system, the present invention adopts linear signal estimation model to construct SO problem, that is:

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

Wherein the size formed for the pixel value of all observation stations corresponding on targeted graphical is the vector of K × 1, and K is observation station number; for light source vector; ICC is the ICC matrix of corresponding all observation stations, and i-th row of ICC, the element of jth row represent light source vector during the spot light of middle jth, at the aerial image intensity that i-th observation station place produces; sized by be the noise vector of K × 1, for characterizing with between error, can be by in each element as having variances sigma ²stochastic variable.Adopt above-mentioned Signal estimation model, the aerial image that after can making optimization, light source is corresponding try one's best in all observation stations at wafer place close to targeted graphical.When aerial image is close to targeted graphical, aerial image distribution has more steep side wall angle, thus is conducive to the side wall angle forming image profiles in more steep photoresist; Meanwhile, it is less that aerial image is distributed in live width difference corresponding on the xsect of differing heights, can reduce the CD error caused by variation of exposure.Therefore, SO problem is configured to the process window that above-mentioned signal estimation problems effectively can expand etching system.

On the other hand, adopt the SO method in the present invention, if obtain newly-increased critical area and the points of measurement certificate after light source optimization terminates, without the need to again optimizing light source, only SELSE method need be adopted to revise current light source optimum results, thus obtain the light source optimum results considering whole critical area and observation station.Meanwhile, the present invention adopts SELSE method, can realize the parallel processing of ICC matrix computations and light source optimization, thus is that the operation efficiency improving existing SO technology further provides possible approaches.

Simultaneously, SO method in the present invention is after acquisition light source optimum results, reverse ORLSE method is adopted to carry out regularization to light source, in each loop iteration, pixel minimum for light intensity in light source is set to 0, and the image error introduced thus is projected on each row of the ICC matrix corresponding to all the other light source points, by revising the intensity of all the other light source points, compensating as far as possible and setting to 0 by above-mentioned light source point the image error caused.Therefore, adopt the method in the present invention to carry out regularization to light source, while reduction light source complexity, raising light source manufacturability, can improve as far as possible or keep the image quality of etching system.

As shown in Figure 1, the present invention adopts the self-adaptation SO method of SELSE and reverse ORLSE, and concrete steps are:

Step 101, light source is initialized as size is N _s× N _slight source figure J, by mask graph M and targeted graphical grid turns to the figure of N × N, and initialization size is N _s ²× N _s ²sELSE covariance matrix Σ, the variances sigma of initialization noise vector ², be an empty matrix by ICC matrix initialisation, be designated as ICC, by vector be initialized as blank vector, wherein a N _sbe integer with N.

Step 102, lining by line scan from upper left to bottom right is carried out to light source figure J, and J is converted into N _s ²the light source vector of × 1 element value be the pixel value of light source figure J.

Step 103, calculate each light source pixel point (x _s, y _s) corresponding x-axis component equivalent point spread function y-axis component equivalent point spread function with z-axis component equivalent point spread function

Step 103 of the present invention calculates light source pixel point (x _s, y _s) corresponding equivalent point spread function with concrete steps be:

Variable predefine

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

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

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

Transformational relation between global coordinate system and local coordinate system:

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

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

Wherein, E _x, E _yand E _zthe component of electric field in global coordinate system that light source sends light wave respectively, E _⊥and E _||be the component of electric field in local coordinate system that light source sends light wave, transition 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, $\mathrm{\&rho;}=\sqrt{{\mathrm{\&alpha;}}^2+{\mathrm{\&beta;}}^2}.$

Calculate equivalent point spread function with concrete steps be:

Step 201, for a single point light source (x _s, y _s), calculate the vector matrix of N × N each element is equal to representative point light source (x _s, y _s) send the electric field intensity of electric field in global coordinate system of light wave.As the light source (x that sets up an office _s, y _s) electric field that sends light wave is expressed as in local coordinate system:

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

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

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

Step 202, for a single point light source (x _s, y _s), calculate the electric field intensity rotation matrix from emergent pupil front to emergent pupil rear wherein be a size be the vector matrix of N × N, each element is the matrix of 3 × 3, can be calculated by (α ', β ', γ ').If with be respectively the Electric Field Distribution at emergent pupil front and rear; α '=cos φ ' sin θ ', β '=sin φ ' sin θ ', γ '=cos θ ', namely optical projection system emergent pupil is incident to the direction cosine (wave vector) of the plane wave of image planes and is φ ' and θ ' is position angle and the elevation angle of wave vector respectively, then with relational expression be:

Wherein, be the vector matrix of a N × N, each element is the 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, for a single point light source (x _s, y _s), calculate the vector matrix of N × N scalar matrix, represent that the numerical aperture of optical projection system is to the limited acceptance ability of diffraction spectrum, the value namely in pupil inside is 1, and the value of pupil outside is 0, is specifically expressed as follows:

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

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

Step 204, to extract respectively in the x durection component of each element y durection component with z durection component obtaining three sizes is the scalar matrix of N × N with

Step 205, by with calculate light source pixel point (x _s, y _s) corresponding equivalent point spread function with p=x, y, z, wherein n _mfor object space medium refraction index, R is the reduction magnification of preferred view system, is generally 4, F ^-1{ } is inverse Fourier transform.

The observation station that one new is selected in step 104, critical area on wafer choose vector middle corresponding observation station element z ^s; Calculate and correspond to observation station new a line of ICC matrix its size is 1 × N _s ², wherein T is matrix transpose operation; Will a line as bottom adds in current ICC matrix; By z ^sadd to current as last element in vector.

Step 104 of the present invention calculates and corresponds to observation station new a line of ICC matrix concrete steps be:

Step 301, light source figure J grid is turned to N _s× N _sindividual pixel, each pixel is as a pointolite.

Step 302, for a single point light source (x _s, y _s), observation station on corresponding wafer when obtaining this spot light aerial image intensity first calculation level light source (x _s, y _s) illumination time corresponding wafer on observation station x, y and z durection component of electric field intensity:

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

The wherein mask graph of M to be size be N × N, the scalar matrix of B to be a size be N × N, be called the diffraction matrices of mask, in B, each element is scalar, and be similar to according to Hopkins (Thelma Hopkins), each element of B can be expressed 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 above formula, pixel represents the length of side of single pixel on mask graph.Then wafer corresponds to observation station aerial image intensity can be expressed as:

Step 303, when judging whether to calculate all spot lights, corresponding to observation station aerial image intensity, if so, then enter step 304, otherwise return step 302.

Step 304, lining by line scan of upper left to bottom right is carried out to light source figure J, and according to scanning sequency by all spot lights time, corresponding to observation station aerial image intensity to be arranged as a size be 1 × N _s ²vector and it can be used as corresponding to observation station new a line of ICC matrix.

Step 105, employing SELSE method, more new light sources vector

SELSE method is adopted, more new light sources vector in step 105 of the present invention detailed process be:

Step 401, calculating size are N _s ²the gain factor of × 1 current SELSE covariance matrix is designated as Σ [n-1], Σ is updated to wherein I is unit matrix.

Step 402, current light source vector to be designated as light source vector is updated to:

Step 403, calculating light source vector in least member value, and to be designated as

Step 404, σ to be updated to: wherein represent light source vector in least member value, the amplification factor of ω > 1 for presetting.

If step 405 then enter step 106, otherwise enter step 406.

Step 406, calculating size are N _s ²the gain factor of × 1 Σ is updated to wherein I is unit matrix.

Step 407, light source vector to be updated to: and will in all pixel values being less than 0 be set to 0.

If step 106 has newly-increased observation station on wafer, then return step 104; Otherwise enter step 107.

Step 107, adopt reverse ORLSE method, the light source vector after computation rule

Reverse ORLSE method is adopted, the light source vector after computation rule in step 107 of the present invention detailed process be:

Step 501, suppose that the observation station of current selection adds up to K, then the size of current ICC matrix is K × N _s ², current vector size be K × 1; Be N from size _s ²the light source vector of × 1 in find all values to equal the element of 0, by these elements from middle deletion, obtains the light source vector that new size is W × 1 row in ICC matrix corresponding to these elements are deleted from ICC matrix, obtains the ICC matrix that new size is K × W, be designated as ICC ^s, wherein W is light source vector in all numbers being greater than the element of 0; Cycle index variable is set to loop=0.

Step 502, determine light source vector in there is the element j of minimum value _minif, j _min<t _sand loop < loop _max, then enter step 503, otherwise enter step 507, wherein t _sand loop _maxbe the threshold value preset.

Step 503, by j _minfrom vector middle deletion, obtains the light source vector that size is (W-1) × 1 by j _mincorresponding ICC ^srow in matrix are designated as will from ICC ^sdelete in matrix, obtain the ICC that new size is K × (W-1) ^smatrix.

Step 504, compute matrix D=(ICC ^sTiCC ^s) ^-1, calculate projection matrix P=I-ICC ^sdICC ^sT, wherein I is unit matrix.

Step 505, design factor: wherein represent vector in the maximal value of each element absolute value, || || ₂represent two norms.

Step 506, by light source vector be updated to: wherein sgn{} is sign function, by obtained in all pixel values being less than 0 be set to 0, be loop+1 by cycle index variable update, and return step 502.

Step 507, termination circulation, and by current light source vector be designated as the vector of the light source after regularization

Embodiment of the present invention:

Be illustrated in figure 3 two critical area schematic diagram on wafer, be also targeted graphical, white represents open area simultaneously, and black representative resistance light region, its critical size is 45nm.Vertically, the lines in critical area shown in 302 in the horizontal direction for lines wherein in critical area shown in 301.

Fig. 4 is primary light source figure, and for the points of measurement certificate on first critical area, the light source figure obtained after adopting SELSE method to be optimized light source.Primary light source shown in 401 is annular light source; 402 is for 2 the points of measurement certificates on first critical area, the result after adopting SELSE method to be optimized light source; 403 is for 7 the points of measurement certificates on first critical area, the result after adopting SELSE method to be optimized light source; 404 is for 100 the points of measurement certificates on first critical area, the result after adopting SELSE method to be optimized light source.

Fig. 5 is the aerial image produced at first critical area place when adopting each light illumination in Fig. 4.501 for light illumination shown in employing 401 time, the aerial image produced at first critical area place; 502 for light illumination shown in employing 402 time, the aerial image produced at first critical area place; 503 for light illumination shown in employing 403 time, the aerial image produced at first critical area place; 504 for light illumination shown in employing 404 time, the aerial image produced at first critical area place.

Fig. 6 is for the points of measurement certificate on second critical area, the light source figure obtained after adopting SELSE method to carry out upgrading optimization further to light source in Figure 40 4.601 is for 1 the points of measurement certificate on second critical area, adopts SELSE method to carry out upgrading further the result after optimizing to light source in 404; 602 is for 50 the points of measurement certificates on second critical area, adopts SELSE method to carry out upgrading further the result after optimizing to light source in 404; 603 is for 90 the points of measurement certificates on second critical area, adopts SELSE method to carry out upgrading further the result after optimizing to light source in 404; 604 is for 100 the points of measurement certificates on second critical area, adopts SELSE method to carry out upgrading further the result after optimizing to light source in 404.

Fig. 7 is at the aerial image that first and second critical area place produce when adopting each light illumination in Fig. 6.701 for light illumination shown in employing 601 time, the aerial image produced at first critical area place; 702 for light illumination shown in employing 601 time, the aerial image produced at second critical area place; 703 for light illumination shown in employing 602 time, the aerial image produced at first critical area place; 704 for light illumination shown in employing 602 time, the aerial image produced at second critical area place; 705 for light illumination shown in employing 603 time, the aerial image produced at first critical area place; 706 for light illumination shown in employing 603 time, the aerial image produced at second critical area place; 707 for light illumination shown in employing 604 time, the aerial image produced at first critical area place; 708 for light illumination shown in employing 604 time, the aerial image produced at second critical area place.

Fig. 8 adopts the SELSE method in the present invention to optimize front and back to light source, the etching system process window comparison diagram that two critical areas are corresponding.801 is when adopting the illumination of the primary light source before optimizing, the process window that first critical area is corresponding; 802 is after adopting the SELSE method in the present invention to be optimized light source, the process window that first critical area is corresponding; 803 is when adopting the illumination of the primary light source before optimizing, the process window that second critical area is corresponding; 804 is after adopting the SELSE method in the present invention to be optimized light source, the process window that second critical area is corresponding.

Fig. 9 is the light source figure before light source regularization, and adopts reverse ORLSE method, carries out the light source figure after different cycle index regularization.901 is the primary light source figure before regularization, consistent with light source shown in 604; 902 is the light source figure obtained after 30 regularization circulation; 903 is the light source figure obtained after 40 regularization circulation; 904 is the light source figure obtained after 51 regularization circulation.

Figure 10 is the aerial image produced at first critical area place when adopting each light illumination in Fig. 9.1001 for light illumination shown in employing 901 time, the aerial image produced at first critical area place; 1002 for light illumination shown in employing 902 time, the aerial image produced at first critical area place; 1003 for light illumination shown in employing 903 time, the aerial image produced at first critical area place; 1004 for light illumination shown in employing 904 time, the aerial image produced at first critical area place.

Figure 11 is the aerial image produced at second critical area place when adopting each light illumination in Fig. 9.1101 for light illumination shown in employing 901 time, the aerial image produced at second critical area place; 1102 for light illumination shown in employing 902 time, the aerial image produced at second critical area place; 1103 for light illumination shown in employing 903 time, the aerial image produced at second critical area place; 1104 for light illumination shown in employing 904 time, the aerial image produced at second critical area place.

Figure 12 adopts the reverse ORLSE method in the present invention to carry out before and after regularization to light source, the etching system process window comparison diagram corresponding to two critical areas.1201 for light illumination without regularization in employing 901 time, the process window that first critical area is corresponding; 1202 for after adopting the ORLSE method in the present invention to carry out regularization to the light source in 901, the process window that first critical area is corresponding; 1203 for light illumination without regularization in employing 901 time, the process window that second critical area is corresponding; 1204 for after adopting the ORLSE method in the present invention to carry out regularization to the light source in 901, the process window that second critical area is corresponding.

Comparison diagram 4-12 is known, and the SO method that the present invention relates to has following effect: the SO method the first, in the present invention effectively can improve the process window of different critical area places etching system.The second, after adopting the SO method in the present invention to be optimized light source, if obtain newly-increased critical area and the points of measurement certificate, without the need to again optimizing light source, and SELSE method can be adopted to revise current light source optimum results, thus obtain the light source optimum results considering whole critical area and observation station.Three, adopt the SO method in the present invention, the parallel processing of ICC matrix computations and light source optimization can be realized.Four, the light source rule method that the present invention relates to while reduction light source complexity, raising light source manufacturability, can improve as far as possible or keeps the image quality of etching system, effectively expand the process window of different critical area places etching system.Five, the present invention utilizes vector imaging model to describe the imaging process of etching system, and the light source figure after optimization is not only applicable to the situation of little NA, is also applicable to the situation of NA>0.6, can meet the simulation requirements of high NA etching system.

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

Claims (5)

1. an adaptive etching system light source optimization method, it is characterized in that, concrete steps are:

Step 101, light source is initialized as size is N _s× N _slight source figure J, by mask graph M and targeted graphical grid turns to the figure of N × N, and initialization size is N _s ²× N _s ²recursive least square estimate (sequentialleastsquareestimator, be called for short SELSE) covariance matrix Σ, the variances sigma of initialization noise vector ², be an empty matrix by illumination interaction coefficent matrix initialisation, be designated as ICC, by vector be initialized as blank vector, wherein a N _sbe integer with N;

Step 102, lining by line scan from upper left to bottom right is carried out to light source figure J, and J is converted into N _s ²the light source vector of × 1 element value be the pixel value of light source figure J;

Step 103, calculate each light source pixel point (x _s, y _s) corresponding x-axis component equivalent point spread function y-axis component equivalent point spread function with z-axis component equivalent point spread function

The observation station that one new is selected in step 104, critical area on wafer choose vector middle corresponding observation station element z ^s; Calculate and correspond to observation station new a line of ICC matrix its size is 1 × N _s ², wherein T is matrix transpose operation; Will a line as bottom adds in current ICC matrix; By z ^sadd to current as last element in vector;

Step 105, employing SELSE method, more new light sources vector

If step 106 has newly-increased observation station on wafer, then return step 104; Otherwise enter step 107;

Step 107, reverse rank recurrence least squares is adopted to estimate (order-recursiveleastsquareestimator is called for short ORLSE) method, the light source vector after computation rule

Step 108, to after regularization light source vector carry out retrograde scan operation, will in each element value be assigned to corresponding N _s× N _sthe pixel of light source figure, and other pixels on light source figure to be set to 0, obtained light source figure are designated as be the light source figure after optimization.

2. a kind of adaptive etching system light source optimization method according to claim 1, it is characterized in that, described step 103 calculates light source pixel point (x _s, y _s) corresponding equivalent point spread function with concrete steps be:

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

Step 201, for a single point light source (x _s, y _s), calculate the vector matrix of N × N if (all elements of a matrix is matrix or vector, be then called vector matrix), each element is equal to representative point light source (x _s, y _s) send the electric field intensity of electric field in global coordinate system of light wave;

Step 202, for a single point light source (x _s, y _s), calculate the electric field intensity rotation matrix from emergent pupil front to emergent pupil rear wherein be a size be the vector matrix of N × N, each element is the matrix of 3 × 3, can be calculated by (α ', β ', γ ');

Step 203, for a single point light source (x _s, y _s), calculate the vector matrix of N × N wherein U is pupil filtering function, each element be the vector of 3 × 1 m, n=1 ... N;

Step 204, to extract respectively in the x durection component of each element y durection component with z durection component obtaining three sizes is the scalar matrix of N × N with

Step 205, by with calculate light source pixel point (x _s, y _s) corresponding equivalent point spread function with

3. a kind of adaptive etching system light source optimization method according to claim 1 or 2, is characterized in that, described step 104 calculates and corresponds to observation station new a line of ICC matrix concrete steps be:

Step 301, light source figure J grid is turned to N _s× N _sindividual pixel, each pixel is as a pointolite;

Step 302, for a single point light source (x _s, y _s), observation station on corresponding wafer when obtaining this spot light aerial image intensity

Step 303, when judging whether to calculate all spot lights, corresponding to observation station aerial image intensity, if so, then enter step 304, otherwise return step 302;

Step 304, lining by line scan of upper left to bottom right is carried out to light source figure J, and according to scanning sequency by all spot lights time, corresponding to observation station aerial image intensity to be arranged as a size be 1 × N _s ²vector and it can be used as corresponding to observation station new a line of ICC matrix.

4. a kind of adaptive etching system light source optimization method according to claim 1 or 2, is characterized in that, adopt SELSE method in described step 105, more new light sources vector detailed process be:

Step 401, calculating size are N _s ²the gain factor of × 1 current SELSE covariance matrix is designated as Σ [n-1], Σ is updated to wherein I is unit matrix;

Step 402, current light source vector to be designated as light source vector is updated to:

Step 403, calculating light source vector in least member value, and to be designated as

Step 404, σ to be updated to: wherein represent light source vector in least member value, the amplification factor of ω > 1 for presetting;

If step 405 then enter step 106, otherwise enter step 406;

Step 406, calculating size are N _s ²the gain factor of × 1 Σ is updated to wherein I is unit matrix;

Step 407, light source vector to be updated to: and will in all pixel values being less than 0 be set to 0.

5. a kind of adaptive etching system light source optimization method according to claim 1 or 2, is characterized in that, adopt reverse ORLSE method in described step 107, the light source vector after computation rule detailed process be:

Step 501, suppose that the observation station of current selection adds up to K, then the size of current ICC matrix is K × N _s ², current vector size be K × 1; Be N from size _s ²the light source vector of × 1 in find all values to equal the element of 0, by these elements from middle deletion, obtains the light source vector that new size is W × 1 row in ICC matrix corresponding to these elements are deleted from ICC matrix, obtains the ICC matrix that new size is K × W, be designated as ICC ^s, wherein W is light source vector in all numbers being greater than the element of 0; Cycle index variable is set to loop=0;

Step 502, determine light source vector in there is the element j of minimum value _minif, j _min<t _sand loop < loop _max, then enter step 503, otherwise enter step 507, wherein t _sand loop _maxbe the threshold value preset;

Step 503, by j _minfrom vector middle deletion, obtains the light source vector that size is (W-1) × 1 by j _mincorresponding ICC ^srow in matrix are designated as will from ICC ^sdelete in matrix, obtain the ICC that new size is K × (W-1) ^smatrix;

Step 504, compute matrix D=(ICC ^sTiCC ^s) ^-1, calculate projection matrix P=I-ICC ^sdICC ^sT, wherein I is unit matrix;

Step 505, design factor: wherein represent vector in the maximal value of each element absolute value, || || ₂represent two norms;

Step 506, by light source vector be updated to: wherein sgn{} is sign function, by obtained in all pixel values being less than 0 be set to 0, be loop+1 by cycle index variable update, and return step 502;

Step 507, termination circulation, and by current light source vector be designated as the vector of the light source after regularization