CN107121893B - Photoetching projection objective lens thermal aberration on-line prediction method - Google Patents
Photoetching projection objective lens thermal aberration on-line prediction method Download PDFInfo
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70591—Testing optical components
- G03F7/706—Aberration measurement
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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- G01M11/0242—Testing optical properties by measuring geometrical properties or aberrations
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Abstract
A kind of photoetching projection objective lens thermal aberration on-line prediction method.This method is in the case where lithographic illumination parameter and mask configuration and work schedule determine, thermal aberration is measured by thermal imagery gap sensor in exposing clearance, the state transition equation of image quality parameter is established based on biexponential model, the thermal aberration of projection objective during particle filter algorithm prediction exposure is utilized with reference to measurement data.Compared to first technology, the present invention more can rapidly and accurately predict the thermal aberration of projection objective.
Description
Technical field
The present invention relates to litho machines, particularly a kind of photoetching projection objective lens thermal aberration on-line prediction method.
Background technology
Litho machine is the Core equipment of great scale integrated circuit manufacture.Projection objective is that litho machine is most complicated, most important
One of subsystem.In the litho machine course of work, the thermal aberration of projection objective can cause image forming quality of photoetching machine to deteriorate, and
Constantly change with the carry out thermal aberration of exposure, characteristic size uniformity (CDU) is caused to decline.Therefore, in every silicon wafer exposure
, it is necessary to which thermal aberration is precisely compensated for even expose before during.In order to ensure effective compensation thermal aberration, quickly and accurately
Thermal aberration on-line prediction technology is indispensable.
2001, ASML report a kind of focal plane based on diexponential function model drift about online Predicting Technique (referring to
First technology 1：Grace H.Ho Anthony T.Cheng,Chung-J.Chen,et al.,“Lens Heating Induced
Focus Drift of i-line Step&Scan:Correction and Control in a Manufacturing
Environment”,Proc.SPIE Vol.4344,0277-786X(2001)).Focal plane heat of the technology based on double-exponential function
Drift model, by a variety of light illumination mode peg model parameters of off-line measurement, by calibrated model application on site in thermal aberration
In compensation.The technical operation is easy, can effectively predict the influence that focal plane drift is brought, but due to off-line measurement process usually and
For actual production environment there are larger difference, precision of prediction is limited.
2012, Can Bikcora et al. proposed a kind of based on diexponential function model and non-linear kalman filtering
The thermal aberration Predicting Technique that algorithm is combined is (referring to first technology 2, Can Bikcora, Martijn van Veelen, Siep
Weiland,et al.,“Lens Heating Induced Aberration Prediction via Nonlinear
Kalman Filters”,IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING,VOL.25,NO.3
(2012)).The technology increases non-linear kalman filtering algorithms on the basis of diexponential function model, realizes on-line measurement
Data to the correction of prediction model and the matching of actual litho machine work schedule, but due to the use of state model exist largely
Pseudo-measurement process, calculating speed is slow, and non-linear kalman filtering algorithms filtering performance in the complicated probability distribution of processing
It is bad.
The content of the invention
It is an object of the invention to provide a kind of lithographic projection objects based on diexponential function model and particle filter algorithm
Mirror thermal aberration on-line prediction method.This method replaces the thermal aberration of phase projection object lens by measuring photo-etching machine silicon chip, with reference to double
Exponential model and particle filter algorithm prediction thermal aberration improve the precision and speed of thermal aberration prediction.
The technical solution of the present invention is as follows：
A kind of photoetching projection objective lens thermal aberration on-line prediction method.The measuring system that this method utilizes includes sharp for generating
The light source of light light beam, lithography illuminating system, for carrying mask and possess the mask platform of precise positioning ability, for by mask artwork
Projection objective system that shape is imaged onto on silicon chip can carry silicon chip and the workpiece with 3-D scanning ability and precise positioning ability
Platform, the thermal imagery gap sensor in the work stage and the data processing computer being connected with sensor.
The light source is traditional lighting, ring illumination, the illumination of two poles, quadrupole illuminating or free lighting source.
The thermal aberration is the Zernike polynomials fitting of the enlargement ratio of projection objective, optimal focal plane or haplopia site.
The image quality parameter that the thermal imagery gap sensor can measure is consistent with the thermal aberration predicted, refers to times magnification
The Zernike polynomials fitting of rate, optimal focal plane or haplopia site.
This method includes the following steps：
1. determine the machine constant of litho machine
The machine constant μ of litho machine1、μ2、τ1、τ2Design with projection objective is closely related, based on experience value choose or
It is determined by off-line calibration method.Off-line calibration method includes two steps：
A. photoetching machine exposure data is measured
Lighting system, lighting parameter, the numerical aperture of litho machine are set, start litho machine.The illumination light that light source is sent is led to
Mask heating projection objective is crossed, until projection objective reaches hot stable state, closing lighting source measures corresponding thermal imagery for lasting illumination
The data that difference changes over time, the thermal imagery difference sequence for measuring M gained areMeasurement time sequence isWherein
K=1 ... M preserve result to computer.
B. computing machine constant
Using nonlinear least square method, object function (1), computing machine constant μ are minimized1、μ2、τ1、τ2。
WhereinFor the thermal aberration numerical value according to model prediction,Meet the equation of following form
2. running litho machine, thermal aberration is measured during silicon chip is replaced
Lighting system, lighting parameter, the numerical aperture of litho machine are set.Start litho machine, load mask and silicon chip, normally
Expose silicon chip.In exposure process, the temperature of projection objective can constantly rise with the progress of exposure, thermal aberration increase.When
After the completion of silicon wafer exposure, stage, no light are replaced into silicon chip, the temperature of projection objective declines, and thermal aberration reduces.When completion one
After the exposure of piece silicon chip, during silicon chip is exchanged, start thermal aberration process of measurement.Using thermal imagery gap sensor in moment tkIt carries out
Kth time measurement, measured value are y (tk), by time of measuring tkWith measurement gained thermal aberration result y (tk) be saved in computer.
3. calculate the estimate of the thermal aberration state parameter of measurement time
The estimate of thermal aberration state parameter is calculated using biexponential model and particle filter algorithm, and wherein particle filter is calculated
The population of method is N.Before measuring for the first time, particle collection is initialized.Initial method is：First, initial point of thermal aberration is set
Cloth p (x0).Then for particle i=1 ... N, according to p (x0) carry out stochastical sampling obtain the initial value of each particle.Each particle
Initial value set into set be particle collection initial value, be expressed asWhereinFor thermal aberration
State parameter initial value, wI, 0It is in for state parameterProbability.
After kth time measurement, for particle i=1 ... N and state j=1,2, following steps are performed：
A. according to state transition equation (3), (4) and tk-1The particle state at momentCalculate tkMoment thermal aberration
The priori estimates of state parameterHeating process state equation is：
Cooling procedure state equation is：
Wherein, x1(tk) and x2(tk) for thermal aberration state parameter, μ1、μ2、τ1、τ2For machine constant, Δ t=tk-tk-1For
The time interval of two states, u1(tk)、u2(tk) it is the sum of random error and compensation rate.Formula (3), (4) describe thermal aberration state
Parameter changes with time rule, virtual condition equation of transfer should according to litho machine work schedule and thermal imagery difference measurements sequential, by
Formula (3) combines acquisition with formula (4).
B. according to state parameterObservational equation (5) and measurement error distribution pvIt calculates and obtains measurement result under the state
ykProbability
y(tk)=x (tk)+ν(tk), (5)
Wherein x (tk) be thermal aberration actual value, ν (tk) it is measurement error, obey distribution pv, actual value x (tk) meet with
Lower equation：
x(tk)=x1(tk)+x2(tk). (6)
C. the probability of all particles is normalized according to formula (7), particle weights W must be normalized by calculatingi,k。
D. the weighted average of thermal imagery state difference parameter is calculated according to formula (8)Posteriority as the state parameter is estimated
Evaluation.
E. number of effective particles is calculated according to formula (9)If number of effective particles is less than threshold value Nmin, resampling.
The resampling is in existing discrete distributionUnder with greater probability replicate the higher particle of weights
The new sampling particle assembly of method generationResampling steps are as follows：
A. normalization weights W is calculated according to formula (10)i,kCumulative distribution collection
B. generate N number of number at random according to being uniformly distributed U (0,1), N number of array into set of random numbers be expressed as
C. according to CDFi,kWithN number of particle is scanned for, when particle l=1 ... N meets CDFi-1,k＜ sl≤CDFi ,kWhen, update resampling value
D. by the weights of whole resampling particlesIt is arranged to
4. calculate the thermal aberration predicted value during exposure
Estimated according to the posteriority of thermal aberration state parameter of formula (3), (4), (6), litho machine work schedule and step 3. gained
EvaluationThermal aberration predicted value in the L cycle of calculated for subsequent, L value ranges be 1≤L≤10, repeat step 2. 3. 4. until
End exposure.
Compared with first technology, the present invention has the following advantages：
1. compared with first technology 1, the present invention extends the type of prediction of thermal aberration, due to considering the work of litho machine
Sequential improves the precision of prediction of thermal aberration.
2. compared with first technology 2, the state transition equation that the present invention uses reduces substantial amounts of pseudo-measurement process, effectively
Ground improves thermal aberration predetermined speed.Due to the use of particle filter algorithm, the present invention is adapted to various errors of form, in complexity
There is better thermal aberration estimated performance in the case of errors of form.
Description of the drawings
Fig. 1 detecting system structure charts of the present invention.
The corresponding litho machine work schedule of Fig. 2 embodiment of the present invention.
The thermal aberration prediction result of Fig. 3 present invention.
Fig. 4 thermal aberration prediction errors of the invention with first technology 1.
Fig. 5 thermal aberration prediction error distribution statistics histograms of the invention with first technology 1.
Specific embodiment
With reference to embodiment and attached drawing, the invention will be further described, but should not limit the present invention with this embodiment
Protection domain.
Fig. 1 is the aberration measurement system that the present invention uses, for generating the light source of laser beam (1), lithography illuminating system
(2), for carrying mask (3) and possess the mask platform (4) of precise positioning ability, for mask graph to be imaged onto on silicon chip
Projection objective system (5), the work stage (6) that can be carried silicon chip and have 3-D scanning ability and precise positioning ability are mounted on
Thermal imagery gap sensor (7) in the work stage and the data processing computer (8) being connected with sensor.
Described light source (1) the present embodiment uses the excimer laser that centre wavelength is 193nm.
The lighting system, the present embodiment use partial coherence factor as [σout,σin]=[0.95,0.75], pole subtended angle
θ=30 °, the anglec of rotation illuminate for two poles of α=0 °.
The numerical aperture of projection objective NA=1.35.
The Section 4 Zernike polynomials fitting Z4 of visual field point centered in described thermal aberration the present embodiment, measurement is in silicon chip every time
It is carried out after end exposure, the thermal aberration of prediction is the Section 4 Zernike polynomials fitting Z4 in next cycle.
The thermal imagery gap sensor (7) is wave aberration sensor, the 4th of visual field point centered on thermal imagery level difference measurements
Item Zernike polynomials fitting Z4.
Machine constant calibration result is in the present embodiment：μ1=18.6nm, μ2=20.3nm, τ1=276s, τ2=1176s,
Calibration process comprises the steps of：
A. photoetching machine exposure data is measured
Parameter setting is carried out to litho machine to be calibrated, lighting system is the illumination of two poles, partial coherence factor [σout,σin]
=[0.95,0.75], pole subtended angle θ=30 °, the anglec of rotation are α=0 °, and numerical aperture NA=1.35 starts litho machine, and light source is sent
Illumination light by mask heat projection objective, persistently illuminate tH=10800s reaches hot stable state to projection objective, closes illumination
Light source, every tM=120s measuring centers visual field point Z4 values measure M=61 times and amount to tC=7200s, the thermal imagery difference sequence of gained
ForMeasurement time sequence isWherein k=1 ... 61 preserves result to computer.
B. computing machine constant
Using nonlinear least square method, object function (1), computing machine constant μ are minimized1、μ2、τ1、τ2：
Wherein,For the thermal aberration numerical value according to model prediction,Meet the equation of following form：
The photoetching projection objective lens thermal aberration on-line prediction stage is comprised the steps of using above system：
1. running litho machine, thermal aberration is measured during silicon chip is replaced：
The lighting system of litho machine is set for the illumination of two poles, partial coherence factor [σout,σin]=[0.95,0.75], pole
Angle θ=30 °, the anglec of rotation be α=0 °, numerical aperture NA=1.35.Start litho machine, load mask and silicon chip, normal exposure 25
Piece silicon chip, work schedule as shown in Fig. 2, the single silicon wafer exposure time beThe changing plate timeWork as completion
After the exposure of a piece of silicon chip, during exchanging silicon chip, after end exposureWhen, start thermal aberration process of measurement, utilize thermal imagery
Gap sensor is in moment tkKth time measurement is carried out, measured value is y (tk), by time of measuring tkWith measurement thermal aberration y (tk) preserve
Into computer.
2. calculate the estimate of the thermal aberration state parameter of measurement time：
The sum of random error and compensation rate in state model u1、u2It obeys respectively and is uniformly distributed u1~U (- 0.5nm,
0.5nm)、u2~U (- 0.5nm, 0.5nm), measurement noise ν Normal Distributions ν~N (0,1nm), the grain of particle filter algorithm
Subnumber N=300, number of effective particles threshold value are Nmin=150.Before measuring for the first time, particle collection is initialized.For particle i=1 ...
N, by the initial prior distribution p (x of thermal aberration0=0)=1 generation sampling particle collectionKth time measurement knot
Shu Hou for particle i=1 ... N and state j=1,2, performs following steps：
A, according to the litho machine work schedule of the present embodiment and thermal imagery difference measurements sequential, the state transition equation measured twice
For formula (3).Use formula (3) and tk-1The particle state at momentCalculate tkThe elder generation of moment particle prediction thermal aberration state parameter
Test estimate
B, according to the estimate of state parameterObservational equation (4) and measurement error distribution N (0,1nm) calculate the state
Obtain measurement result ykProbability be
y(tk)=x (tk)+ν(tk) (4)
Wherein, the actual value x (t of thermal aberrationk) meet below equation：
x(tk)=x1(tk)+x2(tk) (5)
C, the probability of all particles is normalized according to formula (6), particle weights W must be normalized by calculatingi,k：
D, the weighted average of thermal imagery state difference parameter is calculated according to formula (7)Posterior estimate as the state：
E, number of effective particles is calculated according to formula (8)If number of effective particles is less than threshold value Nmin, resampling,
The resampling is in existing discrete distributionUnder weights higher particle sides replicated with greater probability
The new sampling particle assembly of method generationResampling steps are as follows：
A. normalization weights W is calculated according to formula (9)i,kCumulative distribution collection
B. basis is uniformly distributed U (0,1) raw N=300 number at random, and the set of random numbers of 300 numbers compositions is
C. according to CDFi,kWith300 particles are scanned for, when particle l=1 ... N meets CDFi-1,k＜ sl≤
CDFi,kWhen, update resampling value
D. by the weights of whole resampling particlesIt is arranged to
3. calculate the thermal aberration predicted value during exposure：
According to formula (5), (10), (11), (12) and step 2. gained thermal aberration state parameter obtain posterior estimate, count
Calculate the thermal aberration predicted value of follow-up any time.Formula (10), (11), (12) determine such as according to the present embodiment litho machine work schedule
Under：
As 0 ＜ t≤6s,
As 6s ＜ t≤42s,
As 42s ＜ t≤48s,
Wherein, t is the difference of prediction time and measurement time, and 0 ＜ t≤48s.
Repeat 1. 2. 3. step until whole end exposures.
The Ze Nike wave aberration Z4 measurement results of central vision point and prediction result during obtained exposure as shown in figure 3,
Error is predicted as shown in figure 4, thermal aberration prediction error distribution statistics histogram is as shown in figure 5, the formerly prediction of 1 thermal aberration of technology
Average error 0.19nm, standard deviation 0.22nm, this method thermal aberration prediction average error 0.042nm, standard deviation are
0.049nm, total run time are less than 0.05s.
Claims (6)
1. a kind of photoetching projection objective lens thermal aberration on-line prediction method, the measuring system that this method uses includes generating laser
The light source (1) of light beam, lithography illuminating system (2), for carrying mask (3) and possess the mask platform (4) of precise positioning ability, use
In the projection objective system (5) that mask graph is imaged onto on silicon chip, silicon chip can be carried and with 3-D scanning ability and accurately
The work stage (6) of stationkeeping ability, the thermal imagery gap sensor (7) in the work stage and the data being connected with the sensor
Handle computer (8), it is characterised in that this method comprises the following steps：
1. determine the machine constant of litho machine：
Machine constant μ1、μ2、τ1、τ2It chooses or is demarcated by off-line measurement based on experience value, off-line calibration method includes two
Step：
A, litho machine thermal imagery difference data is measured：
Lighting system, lighting parameter, the numerical aperture of litho machine are set, start litho machine, the illumination light that light source is sent is by covering
Mould heats projection objective, and lasting illumination closes lighting source until projection objective reaches hot stable state, measure corresponding thermal aberration with
The data of time change, measure M times, and the thermal imagery difference sequence of gained isMeasurement time sequence isWherein k=
1 ... M preserves result to computer；
B, computing machine constant：
Using nonlinear least square method, object function R equation below (1) is minimized, computing machine constant is μ1、μ2、τ1、τ2,
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2. running litho machine, thermal aberration is measured during silicon chip is replaced：
Lighting system, lighting parameter, the numerical aperture of litho machine are set；Start litho machine, load mask and silicon chip, normal exposure
Silicon chip after the exposure of a piece of silicon chip is completed, during silicon chip is exchanged, is started thermal aberration process of measurement, is sensed using thermal aberration
Device is in moment tkKth time measurement is carried out, measured value is y (tk), by time of measuring tkWith the measured value y (t of corresponding thermal aberrationk)
It is saved in computer；
3. calculate the estimate of the thermal aberration state parameter of measurement time：
The estimate of thermal aberration state parameter calculated using biexponential model and particle filter algorithm, wherein particle filter algorithm
Population is N；Before measuring for the first time, particle collection is initialized；First, the initial distribution of thermal aberration is set as p (x0)；Then for
Particle i=1 ... N, according to p (x0) carry out stochastical sampling obtain the initial value of each particle；The initial value set of each particle into
Set is the initial value of particle collection, is expressed as
Wherein,For the initial value of the state parameter of thermal aberration, wI, 0It is in for state parameterProbability；
After kth time measurement, for particle i=1 ... N and state j=1,2, following steps are performed：
A, according to following heating process state equation (3), cooling procedure state equation (4) and tk-1The particle state at momentMeter
Calculate tkThe priori estimates of moment thermal aberration state parameter
Heating process state equation is：
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<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>-</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
<msub>
<mi>&tau;</mi>
<mn>1</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>-</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
<msub>
<mi>&tau;</mi>
<mn>1</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>-</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
<msub>
<mi>&tau;</mi>
<mn>2</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>-</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
<msub>
<mi>&tau;</mi>
<mn>2</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, x1(tk) and x2(tk) for thermal aberration state parameter, μ1、μ2、τ1、τ2For machine constant, Δ t=tk-tk-1For two shapes
The time interval of state, u1(tk)、u2(tk) it is the sum of random error and compensation rate；Virtual condition equation of transfer should be according to thermal aberration
Sequential is measured, acquisition is combined with formula (4) by formula (3)；
B, according to the priori estimates of thermal aberration state parameterObservational equation (5) and measurement error distribution pvCalculate the state
Lower acquisition measurement result ykProbability
y(tk)=x (tk)+ν(tk), (5)
Wherein, x (tk) be thermal aberration actual value, ν (tk) it is measurement error, obey distribution pv, actual value x (tk) meet with lower section
Journey：
x(tk)=x1(tk)+x2(tk)； (6)
C, normalization particle weights W is calculated according to formula (7)i,k：
<mrow>
<msup>
<mi>W</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msup>
<mo>=</mo>
<mfrac>
<msup>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msup>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msup>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
D, the weighted average of thermal aberration state parameter is calculated according to formula (8)Posteriority as the thermal aberration state parameter is estimated
Evaluation：
<mrow>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mi>j</mi>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msup>
<mi>W</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msup>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msubsup>
<mo>;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
E, number of effective particles is calculated according to formula (9)If number of effective particles is less than threshold value Nmin, resampling；
<mrow>
<msubsup>
<mi>N</mi>
<mrow>
<mi>e</mi>
<mi>f</mi>
<mi>f</mi>
</mrow>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msup>
<mi>W</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
F, the thermal aberration predicted value during exposure is calculated：
Using formula (3), (4), (6), litho machine work schedule and step 2. gained thermal aberration state parameter Posterior estimator
Value calculates the thermal aberration predicted value in kth cycle；
5. repeat the step 2. 3. 4. thermal aberration predicted value in the L cycle of calculated for subsequent.
2. photoetching projection objective lens thermal aberration on-line prediction method according to claim 1, which is characterized in that the light source
It is traditional lighting, ring illumination, the illumination of two poles, quadrupole illuminating or free lighting source.
3. photoetching projection objective lens thermal aberration on-line prediction method according to claim 1, which is characterized in that the thermal imagery
Difference is the Zernike polynomials fitting of enlargement ratio, optimal focal plane or haplopia site.
4. photoetching projection objective lens thermal aberration on-line prediction method according to claim 1, which is characterized in that the thermal imagery
Image quality parameter measured by gap sensor is consistent with the thermal aberration predicted, is enlargement ratio, optimal focal plane or haplopia site
Zernike polynomials fitting.
5. photoetching projection objective lens thermal aberration on-line prediction method according to claim 1, which is characterized in that described adopts again
Quadrat method is in existing discrete distributionUnder the new sampling of weights higher particle method generation replicated with greater probability
Particle assemblyResampling steps are as follows：
A. normalization weights W is calculated according to formula (10)i,kCumulative distribution collection
<mrow>
<msup>
<mi>CDF</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>i</mi>
</munderover>
<msup>
<mi>W</mi>
<mrow>
<mi>q</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
B. generate N number of number at random according to being uniformly distributed U (0,1), N number of array into set of random numbers be expressed as
C. according to CDFi,kWithN number of particle is scanned for, when particle l=1 ... N meetsWhen,
Update resampling value
D. by the weights of whole resampling particlesIt is arranged to
6. photoetching projection objective lens thermal aberration on-line prediction method according to claim 1, which is characterized in that described L
The value range of thermal aberration predicted value in cycle is 1≤L≤10.
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| CN102608870A (en) * | 2011-01-21 | 2012-07-25 | 上海微电子装备有限公司 | Wave aberration measuring device and method |
| CN102735425A (en) * | 2011-04-07 | 2012-10-17 | 上海微电子装备有限公司 | Lens heat effect measuring system and measuring method |
| CN106324995A (en) * | 2015-05-12 | 2017-01-11 | 中国科学院上海光学精密机械研究所 | Photoetching machine in-situ fast high spatial resolution wavefront aberration detection apparatus and photoetching machine in-situ fast high spatial resolution wavefront aberration detection method |
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| CN102608870A (en) * | 2011-01-21 | 2012-07-25 | 上海微电子装备有限公司 | Wave aberration measuring device and method |
| CN102735425A (en) * | 2011-04-07 | 2012-10-17 | 上海微电子装备有限公司 | Lens heat effect measuring system and measuring method |
| CN102184551A (en) * | 2011-05-10 | 2011-09-14 | 东北大学 | Automatic target tracking method and system by combining multi-characteristic matching and particle filtering |
| CN106324995A (en) * | 2015-05-12 | 2017-01-11 | 中国科学院上海光学精密机械研究所 | Photoetching machine in-situ fast high spatial resolution wavefront aberration detection apparatus and photoetching machine in-situ fast high spatial resolution wavefront aberration detection method |
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