CN105785724A - Optimization method for mask pattern, measuring method for optimal focal plane position and system - Google Patents

Abstract

The invention provides an optimization method and system for a mask pattern. An adopted objective function indicates slope of pattern position offset to defocusing amount corresponding to photo-etching space image strength distribution under different defocusing amounts with partial coherent light source illumination and within a preset focus depth scope; the objective function is an evaluation function which is based on photo-etching imaging theory and combined with an optimization algorithm for measuring the sensitivity of the optimal focal plane position of a projection objective system to acquire a mask pattern which has optimized transmittance and phase and is matched with the illuminating mode, so that the measurement sensitivity of the optimal focal plane position under the condition of partial coherent light source illumination can be increased; the mask pattern acquired according to the optimization method is based on the phase shift mask measuring principle; special measurement equipment and complex sensors are not required when the method is used for measuring the optimal focal plane position, so that the measuring cost can be effectively lowered.

Description

The optimization method of a kind of mask pattern, best focal plane position measuring method and system

Technical field

The present invention relates to etching system, particularly to the acquisition methods of a kind of mask pattern, best focal plane position measuring method and system.

Background technology

Litho machine is the visual plant in IC manufacturing, and the performance of litho machine determines the characteristic size of device in IC manufacturing.In litho machine, projection objective system is core component, and its major function is by focusing on realization exposure, thus being imaged onto according to a certain percentage on the object to process by the mask pattern on mask plate.

The depth of focus of the projection objective system of litho machine, in certain scope, develops into 20nm and techniques below node especially with photoetching technique, and the depth of focus of litho machine is at below 60nm.And the size of depth of focus determines the size of imaging, under normal conditions, drift condition can be there is in actual imaging focal plane relative to best focal plane position, detection and the control of focal plane position skew can be carried out by detecting best focal plane position, and then improve photolithographic exposure quality and anti-aliasing degree.

In the prior art, disclose a kind of optical grating construction based on phase-shift mask, the best focal plane position of projection objective system is measured by optical grating construction, but, the method only just can obtain higher measurement sensitivity under the lighting system that partial coherence factor is less, and under in the industry cycle widely used off-axis illumination mode, measure poor sensitivity, it is impossible to obtain satisfied measurement result.In some other method, having good sensitivity, but but need special measurement device and complicated sensing system to complete, testing cost is too high.

Summary of the invention

In view of this, it is an object of the invention to provide the measurement optimization method of a kind of best focal plane, measure highly sensitive and testing cost is low.

For achieving the above object, the present invention has following technical scheme:

A kind of optimization method of mask pattern, described mask pattern is used for the measurement of best focal plane position, including:

S01, it is provided that the transmitance preset of the zones of different on original mask image and phase place, original mask image correspondence phase-shift mask；

S02, set up object function, obtain the target function value under the transmitance and phase place preset, this target function value is current goal functional value, wherein, object function is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount；

S03, with default transmitance and phase place for starting point, optimized algorithm pre-conditioned under, utilize optimized algorithm to obtain the transmitance after optimizing and phase place；

S04, obtains the transmitance after optimizing and the target function value under phase place by object function, and this target function value is optimization object function value；

S05, the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern；

If it is not, then reset the pre-conditioned of optimized algorithm, using the transmitance after optimizing and phase place as default transmitance and phase place, and return step S03.

Alternatively, the surface of light source of partially coherent light source is divided into multiple light source point, the superposition of distribution that described photoetching aerial image intensity is distributed as under each light source point photoetching aerial image intensity.

Alternatively, the surface of light source of partially coherent light source is divided into the method for multiple light source point and includes:

Take the circumscribed square of the surface of light source of partially coherent light source, circumscribed square rasterizing is divided into square subregion, using the central point of each square subregion as a light source point.

Alternatively, optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.

Alternatively, optimized algorithm is simulated annealing, the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place be the transmitance of optimum mask pattern and phase parameter includes:

Judge whether the difference △ f of current goal functional value and optimization object function value is not less than 0, if, it is determined that transmitance after optimization and phase place are transmitance and the phase place of optimum mask pattern；

If △ f is less than 0, then judge e^(△f/T0)Whether more than the random number between 0-1, if, it is determined that transmitance after optimization and phase place are transmitance and phase parameter, the T of optimum mask pattern₀Current Temperatures for simulated annealing.

Alternatively, e is being judged^(△f/T0)Whether also include more than after the random number between 0-1: if less than described random number, then judge whether to meet predetermined end condition, if so, then enter and terminate optimization step.

Additionally, the present invention also provides for the optimization system of a kind of mask pattern, described mask pattern is used for the measurement of best focal plane position, comprising:

Original mask image provides unit, for providing the transmitance preset and phase place, the original mask image correspondence phase-shift mask of the zones of different on original mask image；

Object function sets up unit, is used for setting up object function, and wherein, object function is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount；

Current goal functional value acquiring unit, for obtaining the target function value under default transmitance and phase place, this target function value is current goal functional value；

Optimize unit, for default transmitance and phase place for starting point, optimized algorithm pre-conditioned under, utilize optimized algorithm to obtain the transmitance after optimizing and phase place；

Optimization object function value acquiring unit, for being obtained the transmitance after optimizing and the target function value under phase place by object function, this target function value is optimization object function value；

Optimum mask pattern judging unit, for the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern；

Pre-conditioned reset unit, when not being transmitance and the phase parameter of optimum mask pattern for the transmitance after optimizing and phase place, reset the pre-conditioned of optimized algorithm, and using the transmitance after optimizing and phase place as default transmitance and phase place.

Alternatively, also include light source point division unit, for the surface of light source of partially coherent light source is divided into multiple light source point, the superposition that described photoetching aerial image intensity is distributed as under each light source point the distribution of photoetching aerial image intensity.

Alternatively, in light source point division unit, take the circumscribed square of the surface of light source of partially coherent light source, circumscribed square rasterizing is divided into square subregion, using the central point of each square subregion as a light source point.

Alternatively, optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.

Alternatively, optimized algorithm is simulated annealing, in optimum mask pattern judging unit, it is judged that whether the difference △ f of current goal functional value and optimization object function value is not less than 0, if, it is determined that transmitance after optimization and phase place are transmitance and the phase place of optimum mask pattern；

If △ f is less than 0, then judge e^(△f/T0)Whether more than the random number between 0-1, if, it is determined that transmitance after optimization and phase place are transmitance and phase parameter, the T of optimum mask pattern₀Current Temperatures for simulated annealing.

Alternatively, also include terminating judging unit, for judging e^(△f/T0)After the random number between 0-1, it may be judged whether meet predetermined end condition, if so, then enter and terminate optimizing.

Additionally, the present invention also provides for a kind of best focal plane position measuring method, the mask pattern adopting the transmitance of the optimum mask pattern that the optimization method of any of the above-described mask pattern obtains corresponding with phase parameter carries out the measurement of the best focal plane position.

The optimization method of the mask pattern that the embodiment of the present invention provides and system, the object function adopted is partially coherent light source lighting, the graph position side-play amount that in predetermined focal depth range, under different defocusing amounts, the distribution of photoetching aerial image intensity the is corresponding slope to defocusing amount, this object function is based on optical patterning theory and in conjunction with optimization algorithm, the evaluation function measuring sensitivity with projection objective system the best focal plane position, obtain the mask pattern of the transmitance with optimization and the phase place matched with lighting system, the measurement sensitivity of best focal plane position when can be effectively improved partially coherent light source lighting.Meanwhile, the mask pattern obtained by this optimization method is based on phase-shift mask measuring principle, when being used for the measurement of best focal plane position, it is not necessary to special measurement device and complicated sensor, it is possible to effectively reduce measurement cost.

Further, in the object function set up, the surface of light source of partially coherent light source is divided into multiple light source point, and then the photoetching aerial image intensity under each light source point is distributed the photoetching aerial image intensity distribution being overlapped as under light source lighting, thus the measurement sensitivity of the projection objective system optimal focal plane position being effectively improved under the great photoetching vertical shaft lighting condition in partially coherent light source.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, the accompanying drawing used required in embodiment or description of the prior art will be briefly described below, apparently, accompanying drawing in the following describes is some embodiments of the present invention, for those of ordinary skill in the art, under the premise not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings.

Fig. 1 illustrates the flow chart of the optimization method of mask pattern according to embodiments of the present invention；

Fig. 2 illustrates the cross section structure schematic diagram of the original mask image adopted in optimization method according to embodiments of the present invention；

Fig. 3 illustrates the PHASE DISTRIBUTION schematic diagram in each region of the original mask image of Fig. 2；

Fig. 4 illustrates that the coherent source adopted in the optimization method of the embodiment of the present invention carries out the structural representation after rasterizing；

Fig. 5 illustrates the photoetching aerial image intensity distribution schematic diagram that different defocusing amounts are corresponding in whole focal depth range of the original mask image in an embodiment；

Fig. 6 illustrates the PHASE DISTRIBUTION schematic diagram of the mask pattern that the original mask image of Fig. 5 obtains after optimization；

Fig. 7 illustrates the mask pattern photoetching aerial image intensity distribution schematic diagram that different defocusing amounts are corresponding in whole focal depth range of the optimized rear optimization obtained of the original mask image of Fig. 5；

Fig. 8 illustrates the structural representation of the optimization system of mask pattern according to embodiments of the present invention.

Detailed description of the invention

Understandable for enabling the above-mentioned purpose of the present invention, feature and advantage to become apparent from, below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in detail.

Elaborate a lot of detail in the following description so that fully understanding the present invention, but the present invention can also adopt other to be different from alternate manner described here to be implemented, those skilled in the art can do similar popularization when without prejudice to intension of the present invention, and therefore the present invention is not by the restriction of following public specific embodiment.

Proposing the optimization method of a kind of mask pattern in the present invention, described mask pattern is for the measurement of best focal plane position, and with reference to shown in Fig. 1, the method includes:

S01, it is provided that the zones of different correspondence on original mask image preset transmitance and phase place, original mask image is phase-shift mask；

S02, set up object function, obtain the target function value under the transmitance and phase place preset, this target function value is current goal functional value, wherein, object function is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount；

S03, with default transmitance and phase place for starting point, optimized algorithm pre-conditioned under, utilize optimized algorithm to obtain the transmitance after optimizing and phase place；

S04, obtains the transmitance after optimizing and the target function value under phase place by object function, and this target function value is optimization object function value；

S05, the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern；

If it is not, then reset the pre-conditioned of optimized algorithm, with the transmitance after optimizing and phase place for default transmitance and phase place, and return step S03.

This optimization method can realize in simulation algorithm, for instance simulated annealing can be utilized in matlab to realize, and obtains transmitance and the phase parameter of optimum mask pattern after the optimization, and optimum mask pattern will be used for the measurement of best focal plane position.

In the present invention, the object function adopted is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount, this object function is based on optical patterning theory and in conjunction with optimization algorithm, the evaluation function measuring sensitivity with projection objective system the best focal plane position, obtain the mask pattern of the transmitance with optimization and the phase place matched with lighting system, it is possible to the measurement sensitivity of best focal plane position when being effectively improved partially coherent light source lighting.Meanwhile, the mask pattern that obtained by this optimization method be based on phase-shift mask measuring principle, when being used for the measurement of best focal plane position, it is not necessary to special measurement device and complicated sensor, it is possible to effectively reduce measurement cost.

In order to be better understood from technical scheme and technique effect, below with reference to flow chart, specific embodiment is described in detail.

S01, it is provided that the transmitance preset of the zones of different on original mask image and phase place, original mask image correspondence phase-shift mask.

In the present invention, it is that the optimization method by emulating obtains mask pattern, the mask pattern that original mask image can exist for non-physical, but the relevant parameter of mask pattern, in embodiments of the present invention, original mask image corresponds to interdependent mask, and it exists multiple different region, and each zones of different is correspondingly arranged default transmitance and phase place.

In a specific embodiment, the entity mask pattern that original mask image is corresponding can be the mask pattern of two, referring to figs. 2 and 3 shown, entity mask pattern includes shading layer and these four different regions of the photic zone connected successively, the first phase shift layer and the second phase shift layer, shading layer can be multiple alternatively non-transparent regions with one fixed width, shading layer can be realized by metal material, and metal material is such as crome metal, and the transmitance of shading layer and phase place are all 0；Photic zone, the first phase shift layer and the second phase shift layer can be realized by the opening of the different depth on light transmissive material, light transmissive material can be such as the mask substrate of quartz plate, photic zone can be the region, surface not covering alternatively non-transparent material quartz plate, and its transmitance is 1, and phase place is 0；First phase shift layer can be the opening on quartz plate with first degree of depth, and the degree of depth can be such asThe transmitance of the first phase shift layer is 1, and phase place is 90 °；Second phase shift layer can be the opening on quartz plate with second degree of depth, and the degree of depth can be such asThe transmitance of the second phase shift layer is 1, phase place be 180 ° wherein, λ is the wavelength inciding the light of described test mask in a vacuum, and n is the refractive index of photic zone material, and k is positive integer.For the mask pattern of this entity, in simulation algorithm, it is possible to express by the transmitance preset of the zones of different on original mask image and phase place, it is possible to by this original mask image mask functionExpress, the mould correspondence transmitance of mask function,Value corresponding phase, light blocking district is correspondingValue is π/4, it is necessary to explanation, is 0 for its transmitance of light blocking district, and phase value herein is to ensure that the term amplitude of mask function and transmitance are 0, and this phase value is not really embodied on mask pattern, and transparent area is correspondingValue is 0, and the first phase-shifted region is correspondingValue is pi/2, and the second phase-shifted region is correspondingValue is π.

S02, set up object function, obtain the target function value under the transmitance and phase place preset, this target function value is current goal functional value, wherein, object function is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount.

In the embodiment of the present invention, the optimization method being the condition of analog portion illumination of coherent light source and carry out, partially coherent light source lighting can realize by arranging light source form and coherence factor, the object function built is when partially coherent light source lighting, the graph position side-play amount that in predetermined focal depth range, under different defocusing amounts, the distribution of photoetching aerial image intensity the is corresponding slope to defocusing amount.

Wherein, defocusing amount d is best focal plane position and the real space magnitude of deviation as image space of the projection objective system of litho machine, when defocusing amount d=0, then and corresponding best focal plane position.nullIn a lithography system，Owing to controlling、The existence of the factors such as environment，Cause the position in the deviation ideal image face, imaging surface position of reality，Thus producing defocusing amount d，This defocusing amount d can make the phase place of the light propagated in etching system change，Consider the phase place change of the light that this defocusing amount produces，The Electric Field Distribution at the location of the real image plane place that can be informed under partially coherent light source lighting，And then，The graph position side-play amount that the photoetching aerial image intensity distribution under this defocusing amount is corresponding can be obtained，The position offset of image pattern，The slope of this relative defocusing amount of graph position side-play amount then reflects the graph position side-play amount degree of association to defocusing amount，Mask pattern for different transmitances and phase place，Namely different mask patterns，Then corresponding different slope value，I.e. target function value，The evaluation function measuring sensitivity of best focal plane position it is used as with this slope value，Obtain the mask pattern of optimization，Take into full account that optical patterning is theoretical，The measurement sensitivity of projection objective system the best focal plane position when off-axis illumination can be effectively improved.

In more excellent embodiment, with reference to shown in Fig. 4, for partially coherent light source, its surface of light source 110 can be divided into multiple light source point 130, above-mentioned photoetching aerial image intensity distribution be then the superposition that under each light source point, photoetching aerial image intensity is distributed, the measurement sensitivity of projection objective system optimal focal plane position when to be effectively improved photoetching off-axis illumination.That is, by the surface of light source 110 at source region 100 place of coherent source is divided, thus source region 100 is turned to light source point 130, the illuminant characterization of source region 100 can be expressed by the illuminant characterization of each light source 120, and for the light source point of the non-light source region part on surface of light source 110, illuminant characterization be expressed as 0, non-light source region is the region on surface of light source 110 outside source region 100.

In order to be more fully understood that the object function constructed by the embodiment of the present invention, the process building object function in the Realization of Simulation described in detail below.

First, original mask image grid being turned to multiple subregion, the transmitance of original mask image and phase place use mask function M to represent,

Preferably, physical size according to original mask image and pixel size, it is possible to original mask image grid is turned to N*N sub regions, and N is positive integer, each subregion is an element in simulation calculation matrix, and grid turns to N*N sub regions and is more convenient for simulation calculation.

Then, the surface of light source of partially coherent light source is divided into multiple light source point, with reference to shown in Fig. 4.

Specifically, as shown in Figure 4, surface of light source being divided into Ns*Ns sub regions 120, every sub regions 120 can be square area, the central point (x of every sub regions 120_s,y_s) regard the light source point 130 of this subregion as, thus surface of light source 110 is divided into multiple light source point 130, each light source point 130 is a sampled point, and the illuminant characterization of every sub regions is then with the central point (x of this subregion_s,y_s) intensity of light source at place and polarization state represent, expression formula is E_i(x_s,y_s), for the light source point at the non-light source region place on surface of light source, E_i(x_s,y_s) it is 0.

When carrying out rasterizing, it is possible to adopt the steps to carry out:

Take the circumscribed square of the surface of light source 110 of partially coherent light source.

Circumscribed square rasterizing is divided into square subregion 120, using the central point 130 of each square subregion 120 as a light source point.

The each edge of circumscribed square can being divided into Ns section, thus circumscribed square grid turns to Ns*Ns foursquare subregion, every sub regions can take its central point light source point as this subregion.There is various shape in the surface of light source of the partially coherent light source for adopting in etching system, the method all can be adopted to carry out rasterizing, and in the light source point matrix simply obtained, different light source point coordinate places are not the number difference of 0.

Then, it is thus achieved that object function.

Object function is under partially coherent light source lighting, the graph position side-play amount that in predetermined focal depth range, under different defocusing amounts, the distribution of photoetching aerial image intensity the is corresponding slope to defocusing amount, namely under partially coherent light source, graphically the sensitivity of defocusing amount is object function by position offset, and graph position side-play amount can be obtained by the distribution of photoetching aerial image intensity, it is relevant to defocusing amount and illuminant characterization.The concrete derivation of equation is as follows:

For defocusing amount d, the phase place of the light propagated in etching system being made to change, the change δ of phase place is as follows:

$\mathrm{\δ}=k\·n_w\·d\·(1-{\mathrm{\γ}}^{\′})=k\·n_w\·d\·(1-\sqrt{1-{\mathrm{\α}}^{\′2}-{\mathrm{\β}}^{\′2}})$

Wherein,For wave number, n_wFor the refractive index of optical projection system image space medium, the direction cosines that (α ', β ', γ ') is emergent ray.δ is the scalar matrix of a N × N, and each element representation light wave of certain some phase place change in a lithography system on pupil in matrix, the change of this phase place is caused by out of focus.

When defocusing amount d is 0, wafer is in position, ideal image face, and the Electric Field Distribution on wafer position is shown below:

Wherein, n_wFor the refractive index of optical projection system image space medium, R is the reduction magnification of projection objective system, is generally 4, F^-1{ } represents inverse Fourier transform.⊙ represents homography element multiplication.Low-pass filter function U is the scalar matrix of N × N, represents the numerical aperture limited acceptance ability to diffraction spectrum of optical projection system, is namely 1 in the value within pupil, and the value outside pupil is 0, is specifically expressed as follows:

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

Wherein, (f, g) for world coordinates normalized on entrance pupil.V is the vector matrix of a N × N, and each element is the matrix of 3 × 3:

$V(m,n)=\left[\begin{array}{ccc}\frac{{\mathrm{\β}}^{\′2}+{\mathrm{\α}}^{\′2}{\mathrm{\γ}}^{\′}}{1-{\mathrm{\γ}}^{\′2}}& -\frac{{\mathrm{\α}}^{\′}{\mathrm{\β}}^{\′}}{1+{\mathrm{\γ}}^{\′}}& {\mathrm{\α}}^{\′}\\ -\frac{{\mathrm{\α}}^{\′}{\mathrm{\β}}^{\′}}{1+{\mathrm{\γ}}^{\′}}& \frac{{\mathrm{\α}}^{\′2}+{\mathrm{\β}}^{\′2}{\mathrm{\γ}}^{\′}}{1-{\mathrm{\γ}}^{\′2}}& {\mathrm{\β}}^{\′}\\ -{\mathrm{\α}}^{\′}& -{\mathrm{\β}}^{\′}& {\mathrm{\γ}}^{\′}\end{array}\right],m,n=1,2,\mathrm{...},N$

When defocusing amount d is not 0, it is contemplated that propagate the phase changing capacity δ of light in the etching system caused by non-ideal lithography system defocusing amount d, then in non-ideal lithography system, the Electric Field Distribution on wafer position is expressed as:

Due to E_i(x_s,y_s) in element value unrelated with mask coordinate, so the Electric Field Distribution of wafer position can also be write as:

$E^{wafer}(x_s,y_s)=\frac{2\mathrm{\π}}{n_{w}R}{F}^{-1}\left\{V^{\′}\right\}\⊗M$

Wherein,Represent convolution,For the vector matrix of N × N, each matrix element is the vector (v of 3 × 1_x',v_y',v_z')^T, wherein v_x',v_y',v_z' it is the function of α ' and β '.

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

$E_p^{wafer}(x_s,y_s)=H_p\⊗M$

Wherein,P=x, y, z.V_p' for the scalar matrix of N × N, it is made up of the single coordinate components of each element of vector matrix V'.

Then, as follows for the expression formula of photoetching aerial image intensity distribution under different defocusing amounts:

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

Wherein,Represent matrix delivery squared.This photoetching aerial image intensity is distributed, and namely in the imaging results intensity distributions at wafer position place namely imaging surface place, this formula have expressed the imaging results intensity distributions under different defocusing amount under different light source points, if d=0, is the imaging results distribution of ideal image position.

By this formula so that d=0, calculate different light source point (x respectively_s,y_s) under the imaging results intensity distributions of ideal image position, then, according to Abbe (Abbe) principle, the imaging results intensity under each light source point is overlapped, then can obtain the photoetching aerial image intensity distribution I of ideal image position_bf(x,y,z)。

By this formula so that d is different value, calculate different light source point (x respectively_s,y_s) under the imaging results intensity distributions of different defocusing amount positions, then, similarly, according to Abbe principle, the imaging results intensity under each light source point is overlapped, then can obtain the photoetching aerial image intensity distribution I of different defocusing amount position_def(x,y,z)。

According to Abbe principle, the expression formula of the different defocusing amount position photoetching aerial image intensity distribution after superposition is as follows:

$I_{def}(x,y,z)=\frac{1}{N_s}\underset{{\mathrm{\α}}_s}{\mathrm{\Σ}}\underset{{\mathrm{\β}}_s}{\mathrm{\Σ}}\underset{p=x,y,z}{\mathrm{\Σ}}\left|\right|H_p^{{\mathrm{\α}}_s{\mathrm{\β}}_s}\⊗M|{|}_2^2$

Wherein, N_sIt is the quantity of the light source point of partially coherent light source.Defocusing amount d in above formula is set to 0, the imaging results intensity distributions I at desirable image planes place can be obtained_bf(x,y,z)。

In concrete calculating, can set that predetermined focal depth range, according to certain step change defocusing amount, in a specific embodiment, focal depth range is such as-100nm to 100nm, step-length is 5nm, it is thus achieved that photoetching aerial image intensity distribution after each light source point imaging results distribution superposition under different defocusing amounts, and different defocusing amounts includes the ideal situation of d=0 and d is the situation of other values.

And then, the definition according to map migration amount, the actual imaging position of map migration amount and figure and the magnitude of deviation of ideal position, solve and meet equationX coordinate value, be this photoetching aerial image intensity distribution graph of a correspondence position offset.And graph position side-play amount and d are not graph position side-play amount when 0 during by d=0, obtaining the slope to defocusing amount of the map migration amount under different defocusing amount, this slope can by obtaining the numerical differentiation of graph position side-play amount.

Object function by above-mentioned foundation, first, obtain the target function value under the transmitance and phase place preset, namely obtain and preset the slope value that transmitance is corresponding with object function under the mask function M under phase place, it is thus achieved that the graph position side-play amount of original mask image is relative to the sensitivity of defocusing amount.For the ease of describing, this target function value is denoted as current goal functional value f_cur。

Then, at S03, with default transmitance and phase place for starting point, optimized algorithm pre-conditioned under, utilize optimized algorithm to obtain the transmitance after optimizing and phase place.

Being optimized by optimized algorithm, optimized algorithm can be such as simulated annealing, genetic algorithm, ant group algorithm or gradient algorithm etc., by these optimized algorithms, it is possible to arrange algorithm condition, it is thus achieved that the transmitance more optimized and phase place.

In a specific embodiment, adopt the optimized algorithm of simulated annealing to be optimized, in this optimized algorithm, the pre-conditioned of optimized algorithm, initial temperature T are first set₀Being set to 20 DEG C, final temperature is set to 0.00005 DEG C, attenuation quotient T_ξBeing 0.97, markovian length is 5000.

Then, in step S04, being obtained the transmitance after optimizing and the target function value under phase place by object function, this target function value is optimization object function value.

Object function by above-mentioned foundation, target function value under the transmitance of the optimization obtained in acquisition previous step and phase place, namely obtain the slope value that the transmitance of optimization is corresponding with object function under the mask function M under phase place, obtain the graph position side-play amount sensitivity relative to defocusing amount of the mask pattern optimized, for the ease of describing, this target function value is denoted as optimization object function value f_ref。

Then, in step S05, the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place are transmitance and the phase place of optimum mask pattern.

According to current goal functional value f_curWith optimization object function value f_refDifference △ f, whether the transmitance obtained after determining optimized algorithm optimization and phase place are transmitance and the phase place of optimum mask pattern, wherein, △ f=f_ref-f_cur, different according to the optimized algorithm that adopts, carrying out, according to difference, method that optimum mask pattern determines can also be different.

In the present embodiment, optimized algorithm adopts simulated annealing, in this difference according to current goal functional value and optimization object function value, it is determined that whether transmitance and phase place after optimization are in the optimum transmitance of mask pattern and the step of phase parameter, specifically include:

First, it is determined that whether the difference △ f of current goal functional value and optimization object function value is not less than 0, if, it is determined that transmitance after optimization and phase place are transmitance and the phase place of optimum mask pattern.

If △ f is less than 0, then then judge e^(△f/T0)Whether more than the random number between 0-1, if, it is determined that transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern, and T0 is the Current Temperatures of simulated annealing.

Transmitance and phase place after determining optimization are after optimum mask pattern, then terminate this optimization method, then, set current mask pattern as the mask pattern after optimizing, transmitance, phase place and the optimization object function value that data mask figure is corresponding, the mask pattern after this optimization can be used for the measurement of best focal plane position.

For by the above-mentioned transmitance judged after cannot determining optimization and phase place as after optimum mask pattern, the pre-conditioned of optimized algorithm can be reset, typically require reset pre-conditioned in partial condition, as initial temperature T can be reset in simulated annealing₀And attenuation quotient T_ξDeng, and repeat step S03-S05, new pre-conditioned under re-start optimization and judge, to export optimum mask pattern.

In order to avoid the situation that optimization cannot restrain, namely cannot obtain suitable optimum mask pattern, judge e^(△f/T0)And after the size of the random number between 0-1, if less than described random number, then continue to determine whether to meet predetermined end condition, if, then entering and terminate optimization step, stop this optimization method, predetermined end condition can be determined according to different optimized algorithms, in simulated annealing, predetermined end condition can be Current Temperatures T₀< T_fOr optimize number of times more than predetermined value etc..

The above-mentioned optimization method to the mask pattern of the embodiment of the present invention is described in detail, utilize mask pattern corresponding to the transmitance of the optimum mask pattern that above-mentioned optimization method obtains and phase parameter, it is possible to carry out the measurement of best focal plane position in etching system.

In order to be more fully understood that the technique effect of the optimization method of the present invention, below the simulation result of an instantiation is described in detail.In this specific embodiment, with reference to shown in Fig. 2, the substrate 301 of this original mask image is quartz plate, the region covering metallic chromium layer in substrate 301 is light blocking district 302, transparent area 303 is do not cover metallic chromium layer and expose the region of substrate 301, and the first phase shift layer 304 is the open area that the degree of depth is different in substrate 301 with the second phase shift layer 305；Transparent area 303 is connected with the first phase shift layer 304, and the phase contrast of their transmission light is 90 °；First phase shift layer 304 is connected with the second phase shift layer 305, and the phase contrast of their transmission light is 180 °.Light blocking district 302, transparent area the 302, first phase shift layer 304 and the second phase shift layer 305 width ratio be: 4:1:2:1, the width of the second phase shift layer 305 is 41nm, and the first phase shift layer 304 opening degree of depth isThe second phase shift layer 305 opening degree of depth isλ is the aerial wavelength of incident illumination, and n is the refractive index of described transparency carrier, and k is positive integer.

With reference to shown in Fig. 4, for the partially coherent light source that the present embodiment adopts, this partially coherent light source by being divided into multiple light source point by surface of light source.With reference to shown in Fig. 5, wherein the A in Fig. 5 is the photoetching aerial image intensity distribution that original mask image different defocusing amounts in whole focal depth range are corresponding under this light source lighting system, B is the photoetching aerial image intensity two Distribution value in whole focal depth range under specific threshold, namely by specific threshold value, the photoetching aerial image intensity of the continuous distribution in A is converted into two Distribution value, from B figure it can be seen that, obvious linear relationship is not shown between position offset and the defocusing amount of original mask image, this original mask image is not suitable for the detection of the best focal plane position under this partially coherent light source lighting.

And by above-mentioned original mask image mask pattern after being optimized after optimized algorithm optimization, with reference to shown in Fig. 6, Fig. 6 is phase place and transmitance distribution schematic diagram, one phase place of the Regional Representative of an identical color and the transmitance of the mask pattern obtained after optimizing.With reference to shown in Fig. 7, A in Fig. 7 is the photoetching aerial image intensity distribution that the mask pattern optimized under this partially coherent light source different defocusing amounts in whole focal depth range are corresponding, B is the photoetching aerial image intensity two Distribution value in whole focal depth range under specific threshold, from B figure it can be seen that, its map migration amount is with defocusing amount linear change, by the map migration amount in figure is carried out linear fit, it is possible to obtain the slope of linear relationship between defocusing amount and map migration amount and be about 0.3501.Visible, this mask graph has good detection sensitivity when off-axis illumination, also demonstrates correctness and the effectiveness of optimization method involved in the present invention.

Above the optimization method of the mask pattern of the embodiment of the present invention is described in detail, additionally, present invention also offers the optimization system realizing said method, shown in reference Fig. 8, including:

Original mask image provides unit 200, for providing the transmitance preset and phase place, the original mask image correspondence phase-shift mask of the zones of different on original mask image；

Object function sets up unit 210, is used for setting up object function, and wherein, object function is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount；

Current goal functional value acquiring unit 220, for obtaining the target function value under default transmitance and phase place, this target function value is current goal functional value；

Optimize unit 230, for default transmitance and phase place for starting point, optimized algorithm pre-conditioned under, utilize optimized algorithm to obtain the transmitance after optimizing and phase place；

Optimization object function value acquiring unit 240, for being obtained the transmitance after optimizing and the target function value under phase place by object function, this target function value is optimization object function value；

Optimum mask pattern judging unit 250, for the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern；

Pre-conditioned reset unit 260, when not being transmitance and the phase parameter of optimum mask pattern for the transmitance after optimizing and phase place, reset the pre-conditioned of optimized algorithm, and using the transmitance after optimizing and phase place as default transmitance and phase place.

Further, also include light source point division unit, for the surface of light source of partially coherent light source is divided into multiple light source point, the superposition that described photoetching aerial image intensity is distributed as under each light source point the distribution of photoetching aerial image intensity.

Further, in light source point division unit, take the circumscribed square of the surface of light source of partially coherent light source, circumscribed square rasterizing is divided into square subregion, using the central point of each square subregion as a light source point.

Further, optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.

Further, optimized algorithm is simulated annealing, in optimum mask pattern judging unit 250, it is judged that whether the difference △ f of current goal functional value and optimization object function value is not less than 0, if, it is determined that transmitance after optimization and phase place are transmitance and the phase place of optimum mask pattern；

If △ f is less than 0, then judge e^(△f/T0)Whether more than the random number between 0-1, if, it is determined that transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern, and T0 is the initial temperature of simulated annealing.

Further, also include terminating judging unit, for judging e^(△f/T0)After the random number between 0-1, it may be judged whether meet predetermined end condition, if so, then enter and terminate optimizing.

Each embodiment in this specification all adopts the mode gone forward one by one to describe, between each embodiment identical similar part mutually referring to, what each embodiment stressed is the difference with other embodiments.Especially for system embodiment, owing to it is substantially similar to embodiment of the method, so describing fairly simple, relevant part illustrates referring to the part of embodiment of the method.

The above is only the preferred embodiment of the present invention, although the present invention discloses as above with preferred embodiment, but is not limited to the present invention.Any those of ordinary skill in the art, without departing from, under technical solution of the present invention ambit, may utilize the method for the disclosure above and technology contents and technical solution of the present invention is made many possible variations and modification, or be revised as the Equivalent embodiments of equivalent variations.Therefore, every content without departing from technical solution of the present invention, the technical spirit of the foundation present invention, to any simple modification made for any of the above embodiments, equivalent variations and modification, all still falls within the scope of technical solution of the present invention protection.

Claims (13)

1. an optimization method for mask pattern, described mask pattern is for the measurement of best focal plane position, it is characterised in that including:

S01, it is provided that the transmitance preset of the zones of different on original mask image and phase place, original mask image correspondence phase-shift mask；

S02, set up object function, obtain the target function value under the transmitance and phase place preset, this target function value is current goal functional value, wherein, object function is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount；

S03, with default transmitance and phase place for starting point, optimized algorithm pre-conditioned under, utilize optimized algorithm to obtain the transmitance after optimizing and phase place；

S04, obtains the transmitance after optimizing and the target function value under phase place by object function, and this target function value is optimization object function value；

S05, the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern；

If it is not, then reset the pre-conditioned of optimized algorithm, using the transmitance after optimizing and phase place as default transmitance and phase place, and return step S03.

2. method according to claim 1, it is characterised in that the surface of light source of partially coherent light source is divided into multiple light source point, the superposition of distribution that described photoetching aerial image intensity is distributed as under each light source point photoetching aerial image intensity.

3. method according to claim 2, it is characterised in that the surface of light source of partially coherent light source is divided into the method for multiple light source point and includes:

Take the circumscribed square of the surface of light source of partially coherent light source, circumscribed square rasterizing is divided into square subregion, using the central point of each square subregion as a light source point.

4. method according to claim 1, it is characterised in that optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.

5. method according to claim 1, it is characterized in that, optimized algorithm is simulated annealing, the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place be the transmitance of optimum mask pattern and phase parameter includes:

Judge whether the difference DELTA f of current goal functional value and optimization object function value is not less than 0, if, it is determined that transmitance after optimization and phase place are transmitance and the phase place of optimum mask pattern；

If Δ f is less than 0, then judge e^(Δf/T0)Whether more than the random number between 0-1, if, it is determined that transmitance after optimization and phase place are transmitance and phase parameter, the T of optimum mask pattern₀Current Temperatures for simulated annealing.

6. method according to claim 5, it is characterised in that judging e^(Δf/T0)Whether also include more than after the random number between 0-1: if less than described random number, then judge whether to meet predetermined end condition, if so, then enter and terminate optimization step.

7. an optimization system for mask pattern, described mask pattern is for the measurement of best focal plane position, it is characterised in that including:

Original mask image provides unit, for providing the transmitance preset and phase place, the original mask image correspondence phase-shift mask of the zones of different on original mask image；

Object function sets up unit, is used for setting up object function, and wherein, object function is that in partially coherent light source lighting, predetermined focal depth range, under different defocusing amounts, photoetching aerial image intensity is distributed the corresponding graph position side-play amount slope to defocusing amount；

Current goal functional value acquiring unit, for obtaining the target function value under default transmitance and phase place, this target function value is current goal functional value；

Optimize unit, for default transmitance and phase place for starting point, optimized algorithm pre-conditioned under, utilize optimized algorithm to obtain the transmitance after optimizing and phase place；

Optimization object function value acquiring unit, for being obtained the transmitance after optimizing and the target function value under phase place by object function, this target function value is optimization object function value；

Optimum mask pattern judging unit, for the difference according to current goal functional value and optimization object function value, it is determined that whether transmitance after optimization and phase place are transmitance and the phase parameter of optimum mask pattern；

Pre-conditioned reset unit, when not being transmitance and the phase parameter of optimum mask pattern for the transmitance after optimizing and phase place, reset the pre-conditioned of optimized algorithm, and using the transmitance after optimizing and phase place as default transmitance and phase place.

8. system according to claim 7, it is characterized in that, also include light source point division unit, for the surface of light source of partially coherent light source is divided into multiple light source point, the superposition that described photoetching aerial image intensity is distributed as under each light source point the distribution of photoetching aerial image intensity.

9. system according to claim 8, it is characterized in that, in light source point division unit, take the circumscribed square of the surface of light source of partially coherent light source, circumscribed square rasterizing is divided into square subregion, using the central point of each square subregion as a light source point.

10. system according to claim 7, it is characterised in that optimized algorithm includes simulated annealing, genetic algorithm, ant group algorithm, gradient algorithm.

11. system according to claim 7, it is characterized in that, optimized algorithm is simulated annealing, in optimum mask pattern judging unit, judge whether the difference DELTA f of current goal functional value and optimization object function value is not less than 0, if, it is determined that transmitance after optimization and phase place are transmitance and the phase place of optimum mask pattern；

If Δ f is less than 0, then judge e^(Δf/T0)Whether more than the random number between 0-1, if, it is determined that transmitance after optimization and phase place are transmitance and phase parameter, the T of optimum mask pattern₀Current Temperatures for simulated annealing.

12. system according to claim 11, it is characterised in that also include terminating judging unit, for judging e^(Δf/T0)After the random number between 0-1, it may be judged whether meet predetermined end condition, if so, then enter and terminate optimizing.

13. a best focal plane position measuring method, it is characterized in that, the mask pattern adopting the transmitance of the optimum mask pattern that the optimization method of mask pattern as according to any one of claim 1-6 obtains corresponding with phase parameter carries out the measurement of the best focal plane position.