CN104133348A - Light source optimization method for adaptive photoetching system - Google Patents

Abstract

The invention provides a light source optimization method for an adaptive photoetching system. The aims of optimizing a light source graph, improving the imaging property of the photoetching system and reducing the light source complexity as much as possible are achieved. The light source optimization method adopts a sequential least squares estimation method; the current light source graph is updated by adopting observation point data in a key region in each iteration; after all observation points are traversed, the light source graph is subjected to cyclic regularization by a reverse order recursive least squares estimation method. According to the method, if newly increased observation point data are acquired after light source optimization is finished, the current light source optimization result can be directly corrected, and a light source does not need to be re-optimized; meanwhile, the light source optimization method can realize parallel processing of illumination cross coefficient matrix calculation and light source optimization; furthermore, the complexity of the light source can be reduced, and the imaging quality of the photoetching system is improved or retained as much as possible; finally, with the adoption of a vector imaging model, a simulation precision requirement of a high-NA photoetching system can be met.

Description

A kind of adaptive optical etching system light source optimization method

Technical field

The present invention relates to a kind of employing recursive least square and estimate (sequential least square estimator, be called for short SELSE) and reverse rank recurrence least square estimation (order-recursive least square estimator, abbreviation ORLSE) adaptive optical etching system light source optimization method, belongs to photoetching resolution and strengthens 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 (critical dimension, be called for short CD) constantly reduce and the improving constantly of integrated level, must adopt resolution enhance technology (resolution enhancement technique is called for short RET) to improve imaging resolution and the anti-aliasing degree of etching system.It is a kind of important photoetching resolution enhancing technology that light source is optimized (source optimization is called for short SO).SO technology, by optimizing the light distribution of light source, is modulated the light intensity of the light of incident mask and direction, thereby is improved the corresponding imaging performance of each critical area (hotspot) in full die circuit features.Wherein, critical area refers within the scope of certain technique change, is difficult to the region of possessing higher anti-aliasing degree on as plane.In full die circuit features, generally can comprise a large amount of critical areas with different geometric properties.But, along with constantly dwindling of integrated circuit critical size, the continuous rising of integrated level and overall dimensions, and the introducing with the vector imaging model of higher simulation accuracy, existing SO technology faces data processing amount and computation complexity significantly increases, and the lower problem of operation efficiency.On the other hand, related researcher adopts free form diffractive optical element (freeform diffraction optical elements is called for short DOE) and micro reflector array in the recent period, has realized the SO technology of pixelation.Compare traditional parametrization SO technology, pixelation SO technology has improved greatly light source and has optimized degree of freedom, thus imaging performance that can more efficiently raising etching system.But the light source optimum results that adopts pixelation SO technology to obtain often has higher complexity, thereby has reduced the manufacturability of light source.Therefore, how to reduce and optimize the complexity of rear light source, the manufacturability of raising light source becomes one of major issue in pixelation SO technology.

Pertinent literature (Optics Express, 2014,22 (12): 14180-14198) adopt compressed sensing (compressive sensing is called for short CS) technology to propose a kind of SO method that operation efficiency is higher.The method is demarcated some observation stations at wafer place, is optimized and is made the imaging at these observation station places as far as possible close to targeted graphical, thereby improve the image quality in whole image planes by SO.The etching system aerial image model that the method adopts is: wherein the vector forming for the aerial image light intensity value at all pixels place on wafer, vector for obtaining after light source figure is lined by line scan, is called light source vector, and ICC is illumination interaction coefficent (illumination cross coefficient is called for short ICC) matrix.First the method need to calculate complete ICC matrix, according to above-mentioned imaging model, light source is optimized afterwards.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 for the selected observation station of all critical areas, calculates afterwards the complete ICC matrix corresponding to all observation stations.After light source optimization finishes, 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, then again light source are optimized.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 be calculated complete ICC matrix before light source is optimized, thereby cannot use parallel computation mode to carry out the calculating of ICC matrix and the optimization of light source, thereby limited the further lifting of this algorithm operation efficiency simultaneously.In sum, existing SO method cannot be according to newly-increased critical area and observation station, and the existing light source optimum results of adaptive renewal cannot be realized the parallel processing that ICC matrix computations and light source are optimized simultaneously, is further improved.

On the other hand, pertinent literature (Applied Optics, 2013,52 (18): 4200-4211) proposed a kind of rule method for reducing light source optimum results complexity.The method is after light source optimization finishes, and the light source pixel that first all light intensity is less than to predetermined threshold sets to 0.Afterwards, all light source pixels of searching loop, for each light source pixel, if non-zero pixels number is less than 3 in 8 light source pixels that are adjacent, set to 0 this light source pixel.Yet the method, when reducing light source figure complexity, is not considered the impact of light source simplification on etching system imaging performance.Therefore, existing light source rule method, when reducing light source complexity, is difficult to improve or keep the image quality of etching system, is further improved.

Summary of the invention

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

An adaptive optical etching system light source optimization method, concrete steps are:

Step 101, light source is initialized as to size for 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, ICC matrix is initialized as to an empty matrix, be designated as ICC, by vector be initialized as blank vector, wherein a N _swith N be integer;

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

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

In step 104, the critical area on wafer, select a new observation station choose vector middle corresponding observation station element z ^s; Calculating is corresponding to observation station new a line of ICC matrix its size is 1 * N _s ², wherein T is matrix transpose operation; Will as a line of below, add in current ICC matrix; By z ^sas last element, add to current in vector;

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

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

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

Step 108, vectorial to the light source after regularization the scan operation of driving in the wrong direction, 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 are set to 0, obtained light source figure is designated as be the light source figure after optimization.

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

The direction of setting optical axis is z axle, and sets up global coordinate system according to left-handed coordinate system principle; (α, beta, gamma) is that global coordinate system on mask (x, y, z) carries out the coordinate system after 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), the vector matrix of calculating N * N each element is equal to representative point light source (x _s, y _s) electric field intensity of electric field in global coordinate system that send light wave;

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

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

Step 204, extraction respectively in the x durection component of each element y durection component with z durection component obtain three scalar matrixs that size is N * N with

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

Step 104 of the present invention is calculated corresponding 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 while obtaining this spot light aerial image intensity

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

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

In step 105 of the present invention, adopt SELSE method, more new light sources vector detailed process be:

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

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

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

Step 404, σ is updated to: wherein represent light source vector in least member value, ω > 1 is predefined amplification factor;

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

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

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

In step 107 of the present invention, adopt reverse ORLSE method, the light source vector after computation rule detailed process be:

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

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

Step 503, general from vector middle deletion, obtaining size is the light source vector of (W-1) * 1 will corresponding ICC ^srow in matrix are designated as will from ICC ^sin matrix, delete, obtain new size and be the ICC of K * (W-1) ^smatrix;

Step 504, compute matrix D=(ICC ^sTiCC ^s) ^-1, calculate projection matrix P=I-ICC ^sd ICC ^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, light source is vectorial be updated to: wherein sgn{} is sign function, by obtained in all pixel values of 0 of being less than be set to 0, by cycle index variable update, be loop+1, and return to step 502;

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

Beneficial effect of the present invention:

The first, the SO method 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 finishes, without light source is optimized again, and can adopt SELSE method to revise current light source optimum results, thereby obtain the light source optimum results of having considered whole critical areas and observation station.

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

The 3rd, the present invention adopts reverse ORLSE method to carry out regularization to light source figure.In each loop iteration, the pixel of light intensity minimum in light source is set to 0, and the image error of introducing is thus projected to respectively listing of the corresponding ICC matrix of all the other light source points, by revising the intensity of all the other light source points, compensation sets to 0 by above-mentioned light source point the image error causing as far as possible.Therefore, the light source rule method in the present invention can, when reducing light source complexity, improving light source manufacturability, improve or keep as far as possible the image quality of etching system.

Finally, the present invention utilizes vector imaging model to describe the imaging process of etching system, considered 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, can meet the simulation accuracy requirement of high NA etching system.

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 that the light wave that pointolite sends forms the schematic diagram of 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 obtaining after employing SELSE method is optimized light source.

The aerial image that Fig. 5 produces 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, adopts SELSE method to carry out further upgrading to light source in Figure 40 4 the light source figure obtaining after optimization.

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

Fig. 8 is for adopting the SELSE method in the present invention to optimize front and back, two etching system process window comparison diagrams that critical area is corresponding to light source.

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.

The aerial image that Figure 10 produces at first critical area place when adopting each light illumination in Fig. 9.

The aerial image that Figure 11 produces at second critical area place when adopting each light illumination in Fig. 9.

Figure 12 is for adopting the reverse ORLSE method in the present invention to carry out regularization front and back, two the corresponding etching system process window of critical area comparison diagrams to light source.

Embodiment

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

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

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

Wherein for the vector that size is K * 1 that the pixel value of corresponding all observation stations on targeted graphical forms, K is observation station number; for light source vector; ICC is the ICC matrix of corresponding all observation stations, and the i element capable, j row of ICC represents light source vector during j spot light, the aerial image intensity producing at i observation station place; for the size noise vector that is K * 1, for characterizing with between error, can be by in each element as thering is variances sigma ²stochastic variable.Adopt above-mentioned Signal estimation model, can make to optimize the targeted graphical that approaches that aerial image that rear light source is corresponding tries one's best in all observation stations at wafer place.When aerial image approaches targeted graphical, aerial image distributes and has more steep side wall angle, thereby is conducive to form the side wall angle of imaging profile in more steep photoresist; Meanwhile, it is less that aerial image is distributed in live width difference corresponding on the xsect of differing heights, the CD error that can reduce to be caused by variation of exposure.Therefore, SO problem is configured to the process window that above-mentioned signal estimation problems can effectively be expanded 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 finishes, without light source is optimized again, only need to adopt SELSE method to revise current light source optimum results, thereby obtain the light source optimum results of considering whole critical areas and observation station.Meanwhile, the present invention adopts SELSE method, can realize the parallel processing that ICC matrix computations and light source are optimized, thereby provides possible approaches for further improving the operation efficiency of existing SO technology.

Simultaneously, SO method in the present invention is after obtaining light source optimum results, adopt reverse ORLSE method to carry out regularization to light source, in each loop iteration, the pixel of light intensity minimum in light source is set to 0, and the image error of introducing is thus projected to respectively listing of the corresponding ICC matrix of all the other light source points, by revising the intensity of all the other light source points, compensation sets to 0 by above-mentioned light source point the image error causing as far as possible.Therefore, adopt the method in the present invention to carry out regularization to light source, can, when reducing light source complexity, improving light source manufacturability, improve or keep as far as possible 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 to size for 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, ICC matrix is initialized as to an empty matrix, be designated as ICC, by vector be initialized as blank vector, wherein a N _swith N be integer.

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

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

Step 103 of the present invention is calculated light source pixel (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 axle, and with z axle, sets up global coordinate system (x, y, z) according to left-handed coordinate system principle; If the world coordinates of any point light source is (x on partial coherence light source face _s, y _s, z _s), the direction cosine of being sent and be incident to the plane wave of mask by this pointolite are (α _s, β _s, γ _s), 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 space numerical aperture.

If the world coordinates of any point is (x on mask, y, z), based on diffraction principle, the direction cosine that are incident to the plane wave of optical projection system entrance pupil from mask are (α, beta, gamma), (α wherein, β, γ) that the upper global coordinate system (x, y, z) of mask (object plane) carries out the coordinate system after 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 that are 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 the emit beam direction of vibration of middle TE polarized light of light source, e _||axle is the emit beam direction of vibration of middle TM polarized light of light source.Wave vector is the plane consisting 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.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 _zrespectively the component of electric field in global coordinate system that light source sends light wave, 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), the vector matrix of calculating N * N each element is equal to representative point light source (x _s, y _s) electric field intensity of electric field in global coordinate system that send 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:

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

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 the place ahead to emergent pupil rear wherein be a vector matrix that size is N * N, the matrix that each element is 3 * 3, can be calculated by (α ', β ', γ ').If with be respectively the Electric Field Distribution at emergent pupil the place ahead and rear; α '=cos φ ' sin θ ', β '=sin φ ' sin θ ', γ '=cos θ ', 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 ' are respectively position angle and the elevations angle of wave vector, 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), the vector matrix of calculating N * N scalar matrix, the limited receiving ability of the numerical aperture of expression optical projection system to diffraction spectrum, the value in pupil inside is 1, 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 normalized world coordinates on entrance pupil.

Step 204, extraction respectively in the x durection component of each element y durection component with z durection component obtain three scalar matrixs that size is N * N with

Step 205, by with calculate light source pixel (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.

In step 104, the critical area on wafer, select a new observation station choose vector middle corresponding observation station element z ^s; Calculating is corresponding to observation station new a line of ICC matrix its size is 1 * N _s ², wherein T is matrix transpose operation; Will as a line of below, add in current ICC matrix; By z ^sas last element, add to current in vector.

Step 104 of the present invention is calculated corresponding 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 while obtaining this spot light aerial image intensity first calculation level light source (x _s, y _s) observation station on when illumination corresponding wafer x, y and the 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

Wherein M is that size is the mask graph of N * N, and B is that a size is the scalar matrix of N * N, is called the diffraction matrices of mask, and in B, each element is scalar, and approximate 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.On wafer corresponding to observation station aerial image intensity can be expressed as:

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

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

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

In step 105 of the present invention, adopt SELSE method, more new light sources vector detailed process be:

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

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

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

Step 404, σ is updated to: wherein represent light source vector in least member value, ω > 1 is predefined amplification factor.

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

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

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

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

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

In step 107 of the present invention, adopt reverse ORLSE method, the light source vector after computation rule detailed process be:

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

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

Step 503, by j _minfrom vector middle deletion, obtaining size is the light source vector of (W-1) * 1 will corresponding ICC ^srow in matrix are designated as will from ICC ^sin matrix, delete, obtain new size and be the ICC of K * (W-1) ^smatrix.

Step 504, compute matrix D=(ICC ^sTiCC ^s) ^-1, calculate projection matrix P=I-ICC ^sd ICC ^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, light source is vectorial be updated to: wherein sgn{} is sign function, by obtained in all pixel values of 0 of being less than be set to 0, by cycle index variable update, be loop+1, and return to step 502.

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

Embodiment of the present invention:

Be illustrated in figure 3 two critical area schematic diagram on wafer, be also targeted graphical simultaneously, and white represents open area, black representative resistance light region, and its critical size is 45nm.Wherein the lines in critical area shown in 301 vertically, the lines along continuous straight runs shown in 302 in critical area.

Fig. 4 is primary light source figure, and for the points of measurement certificate on first critical area, the light source figure obtaining after employing SELSE method is 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, adopts the result after SELSE method is optimized light source; 403 is for 7 the points of measurement certificates on first critical area, adopts the result after SELSE method is optimized light source; 404 is for 100 the points of measurement certificates on first critical area, adopts the result after SELSE method is optimized light source.

The aerial image that Fig. 5 produces at first critical area place when adopting each light illumination in Fig. 4.501 is while adopting light illumination shown in 401, the aerial image producing at first critical area place; 502 is while adopting light illumination shown in 402, the aerial image producing at first critical area place; 503 is while adopting light illumination shown in 403, the aerial image producing at first critical area place; 504 is while adopting light illumination shown in 404, the aerial image producing at first critical area place.

Fig. 6 is for the points of measurement certificate on second critical area, adopts SELSE method to carry out further upgrading to light source in Figure 40 4 the light source figure obtaining after optimization.601 is for 1 the points of measurement certificate on second critical area, adopts SELSE method to carry out further upgrading 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 further upgrading 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 further upgrading 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 further upgrading the result after optimizing to light source in 404.

Fig. 7 when adopting in Fig. 6 each light illumination at first and second aerial image that critical area place produces.701 is while adopting light illumination shown in 601, the aerial image producing at first critical area place; 702 is while adopting light illumination shown in 601, the aerial image producing at second critical area place; 703 is while adopting light illumination shown in 602, the aerial image producing at first critical area place; 704 is while adopting light illumination shown in 602, the aerial image producing at second critical area place; 705 is while adopting light illumination shown in 603, the aerial image producing at first critical area place; 706 is while adopting light illumination shown in 603, the aerial image producing at second critical area place; 707 is while adopting light illumination shown in 604, the aerial image producing at first critical area place; 708 is while adopting light illumination shown in 604, the aerial image producing at second critical area place.

Fig. 8 is for adopting the SELSE method in the present invention to optimize front and back, two etching system process window comparison diagrams that critical area is corresponding to light source.801 during for primary light source illumination before adopt optimizing, the process window that first critical area is corresponding; 802 for after adopting SELSE method in the present invention to be optimized light source, the process window that first critical area is corresponding; 803 during for primary light source illumination before adopt optimizing, second process window that critical area is corresponding; 804 for after adopting SELSE method in the present invention to be optimized light source, second process window that 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 for the primary light source figure before regularization, consistent with light source shown in 604; 902 is the light source figure obtaining after 30 regularization circulation; 903 is the light source figure obtaining after 40 regularization circulation; 904 is the light source figure obtaining after 51 regularization circulation.

The aerial image that Figure 10 produces at first critical area place when adopting each light illumination in Fig. 9.1001 is while adopting light illumination shown in 901, the aerial image producing at first critical area place; 1002 is while adopting light illumination shown in 902, the aerial image producing at first critical area place; 1003 is while adopting light illumination shown in 903, the aerial image producing at first critical area place; 1004 is while adopting light illumination shown in 904, the aerial image producing at first critical area place.

The aerial image that Figure 11 produces at second critical area place when adopting each light illumination in Fig. 9.1101 is while adopting light illumination shown in 901, the aerial image producing at second critical area place; 1102 is while adopting light illumination shown in 902, the aerial image producing at second critical area place; 1103 is while adopting light illumination shown in 903, the aerial image producing at second critical area place; 1104 is while adopting light illumination shown in 904, the aerial image producing at second critical area place.

Figure 12 is for adopting the reverse ORLSE method in the present invention to carry out regularization front and back, two the corresponding etching system process window of critical area comparison diagrams to light source.1201 is while not passing through the light illumination of regularization in employing 901, the process window that first critical area is corresponding; 1202 for adopting the ORLSE method in the present invention to carry out after regularization the light source in 901, the process window that first critical area is corresponding; 1203 is while not passing through the light illumination of regularization in employing 901, second process window that critical area is corresponding; 1204 for adopting the ORLSE method in the present invention to carry out after regularization the light source in 901, second process window that critical area is corresponding.

Comparison diagram 4-12 is known, and the SO method the present invention relates to has following effect: the first, the SO method in the present invention can effectively improve the process window of different critical areas place etching system.The second, after the SO method in employing the present invention is optimized light source, if obtain newly-increased critical area and the points of measurement certificate, without light source is optimized again, and can adopt SELSE method to revise current light source optimum results, thereby obtain the light source optimum results of having considered whole critical areas and observation station.Three, adopt the SO method in the present invention, can realize the parallel processing that ICC matrix computations and light source are optimized.Four, the light source rule method the present invention relates to can improve or keep as far as possible the image quality of etching system when reducing light source complexity, improving light source manufacturability, effectively expands the process window of different critical areas place 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.

Although combine accompanying drawing, the specific embodiment of the present invention has been described; 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, is characterized in that, concrete steps are:

Step 101, light source is initialized as to size for 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 (sequential least square estimator is called for short SELSE) covariance matrix Σ, the variances sigma of initialization noise vector ², ICC matrix is initialized as to an empty matrix, be designated as ICC, by vector be initialized as blank vector, wherein a N _swith N be integer;

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

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

In step 104, the critical area on wafer, select a new observation station choose vector middle corresponding observation station element z ^s; Calculating is corresponding to observation station new a line of ICC matrix its size is 1 * N _s ², wherein T is matrix transpose operation; Will as a line of below, add in current ICC matrix; By z ^sas last element, add to current in vector;

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

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

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

Step 108, vectorial to the light source after regularization the scan operation of driving in the wrong direction, 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 are set to 0, obtained light source figure is designated as be the light source figure after optimization.

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

The direction of setting optical axis is z axle, and sets up global coordinate system according to left-handed coordinate system principle; (α, beta, gamma) is that global coordinate system on mask (x, y, z) carries out the coordinate system after 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), the vector matrix of calculating N * N if (all elements of a matrix is matrix or vector, is called vector matrix), each element is equal to representative point light source (x _s, y _s) electric field intensity of electric field in global coordinate system that send light wave;

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

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

Step 204, extraction respectively in the x durection component of each element y durection component with z durection component obtain three scalar matrixs that size is N * N with

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

3. according to a kind of adaptive etching system light source optimization method described in claim 1 or 2, it is characterized in that, described step 104 is calculated corresponding 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 while obtaining this spot light aerial image intensity

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

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

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

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

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

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

Step 404, σ is updated to: wherein represent light source vector in least member value, ω >1 is predefined amplification factor;

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

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

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

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

Step 501, suppose that the observation station of current selection adds up to K, the size of current ICC matrix is K * N _s ², current vector size be K * 1; From size, be N _s ²* 1 light source vector in find all values to equal 0 element, by these elements from middle deletion, obtaining new size is the light source vector of W * 1 row in the corresponding ICC matrix of these elements are deleted from ICC matrix, and obtaining new size is the ICC matrix of K * W, is designated as ICC ^s, wherein W is light source vector in all numbers that are greater than 0 element; Cycle index variable is made as 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, enter step 503, otherwise enter step 507, wherein t _sand loop _maxbe predefined threshold value;

Step 503, by j _minfrom vector middle deletion, obtaining size is the light source vector of (W-1) * 1 by j _mincorresponding ICC ^srow in matrix are designated as will from ICC ^sin matrix, delete, obtain new size and be the ICC of K * (W-1) ^smatrix;

Step 504, compute matrix D=(ICC ^sTiCC ^s) ^-1, calculate projection matrix P=I-ICC ^sd ICC ^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, light source is vectorial be updated to: wherein sgn{} is sign function, by obtained in all pixel values of 0 of being less than be set to 0, by cycle index variable update, be loop+1, and return to step 502;

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