CN103106331A - Photo-etching line width intelligence forecasting method based on dimension-reduction and quantity-increment-type extreme learning machine - Google Patents

Photo-etching line width intelligence forecasting method based on dimension-reduction and quantity-increment-type extreme learning machine Download PDF

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CN103106331A
CN103106331A CN2012105437716A CN201210543771A CN103106331A CN 103106331 A CN103106331 A CN 103106331A CN 2012105437716 A CN2012105437716 A CN 2012105437716A CN 201210543771 A CN201210543771 A CN 201210543771A CN 103106331 A CN103106331 A CN 103106331A
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刘民
郝井华
郭路
吴澄
王凌
张亚斌
刘涛
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Tsinghua University
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Abstract

The invention provides a photo-etching line width intelligence forecasting method based on a dimension-reduction and quantity-increment-type extreme learning machine, belongs to the field of automatic control, information technology and advanced manufacturing, and particularly relates to a method that special to the characteristic that training data are high in dimensionality and arrives in a batching mode in the modeling process of a photo-etching line width index, intelligent online forecasting of the photo-etching line width index is achieved by conducting matrix inversion and dimension reduction to a batching extreme learning machine based on minimizing of structural risks. The photo-etching line width intelligence forecasting method based on the dimension-reduction and quantity-increment-type extreme learning machine is characterized by comprising the following steps: matrix inversion in the batching extreme learning machine based on the minimizing of structural risks is conducted dimension reduction by adopting a matrix inversion dimension reduction formula to build the relations between model parameters of the extreme learning machine and new-arriving data, and online increment-quantity-type leaning and updating of output layer weights of the model parameters of the extreme learning machine are achieved. The index forecasting method which is used for the dimension-reduction and quantity-increment-type extreme learning machine and based on matrix inversion dimension reduction has good forecasting effect.

Description

Lithographic line width Intelligent Forecasting based on dimensionality reduction and increment type extreme learning machine
Technical field
The invention belongs to automatic control, infotech and advanced manufacturing field, for in characteristics high to the existing data dimension of lithographic line width forecasting process and that training data arrives in batches, a kind of lithographic line width Intelligent Forecasting that obtains online increment type extreme learning machine based on the matrix inversion dimensionality reduction is proposed, it can realize the online adjustment to the index prediction model parameter, and the method has precision of prediction and efficient preferably.
Background technology
Lithographic line width is the critical process index that affects the microelectronic product yield, but its testing result exists than large time delay at present, be difficult to realize the on-line optimization adjustment on the relevant critical process operating parameter that affects this index, thereby affected the improvement of product yield, thereby needed the real-time estimate of realizing the lithographic line width index badly in the microelectronics production line.Have the advantages that for the data that obtain in the lithographic line width testing process dimension is high, data arrive in batches, propose a kind of lithographic line width prediction algorithm based on matrix inversion dimensionality reduction and increment type extreme learning machine.In recent years, the multiple neural net methods that can be used for the nonlinear system line modeling such as GAP-RBF, SAO-ELM, OS-ELM have been suggested, these class methods can be when new data arrive, structure or parameter to model are adjusted online, thereby avoid all sample datas are trained again, reduce calculated amount, improved counting yield.But carry out modeling because said method all is based on the empirical risk minimization criterion, have the defectives such as over-fitting, hidden node are difficult to determine, the modeling accuracy when having a strong impact on practical application.How improving precision and the efficient of modeling algorithm, satisfy simultaneously the characteristics that data arrive in batches, is the difficult point of setting up the lithographic line width forecast model.Index prediction method based on matrix inversion dimensionality reduction and increment type extreme learning machine proposed by the invention has prediction effect preferably to the lithographic line width index.
Summary of the invention
In order to solve above-mentioned difficult point, the present invention proposes a kind of lithographic line width Intelligent Forecasting based on the conversion of matrix inversion dimensionality reduction and increment type extreme learning machine, to adopt matrix inversion dimensionality reduction formula to carry out dimensionality reduction based on the matrix inversion in the batch processing extreme learning machine of structural risk minimization, to set up extreme learning machine model parameter and the new relation that arrives data, realize online incremental learning and output layer right value update to the extreme learning machine model parameter.
Lithographic line width Intelligent Forecasting based on dimensionality reduction and increment type extreme learning machine is characterized in that, described method is to realize according to the following steps successively on computers:
Step (1): Model Selection and parameter initialization
For a given N sample, its input is designated as
Figure BSA00000823698800021
X wherein iRepresent the vector that every i sample is comprised of 29 dimension data, this vector comprises following parameter: be in quality control value, wire width measuring value and the photoresist thickness of exposure dose corresponding to front 5 lot of identical processing level, same breed, focal length of photoetching machine, exposure dose with lot to be predicted; The quality control value of the exposure dose of current lot to be predicted, focal length of photoetching machine, exposure dose and photoresist thickness; N the corresponding output of sample input is designated as
Figure BSA00000823698800022
y iBe the lithographic line width measured value;
The number of hidden nodes L of given extreme learning machine based on structural risk minimization adopts radial basis function as the eigentransformation function, and functional form is G ( a i , b i , x i ) = e - b i ( | | x i - a i | | ) , i = 1,2 , · · · , L , A wherein i, b iBe the parameter of radial basis function, a iDimension is 29 dimensions, and it can be chosen from [1 1] at random, b iBe 1 the dimension, value be from 1 100 13 300 Choose at random;
So the extreme learning machine Feature Mapping matrix H (X) of generation is:
H ( X ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N ) G ( a 2 , b 2 , x N ) · · · G ( a L , b L , x N )
Step (2): algorithm initialization
For moment t, the weighting parameter W of increment type extreme learning machine tInitialization value is:
W t = [ 1 v + H ( X t ) T H ( X t ) ] - 1 H ( X t ) T Y t
Wherein:
X tThe sample that expression t has obtained constantly, sample size is N, so the extreme learning machine mapping matrix that produces is:
H ( X t ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N ) G ( a 2 , b 2 , x N ) · · · G ( a L , b L , x N )
Y t = y 1 y 2 · · · y N
V adopts empirical value for the compromise coefficient, is taken as 2 -15
Step (3): on-line study process
For t+1 constantly, the quantity of supposing new arrival sample is k, newly arrives corresponding being input as of sample
Figure BSA00000823698800029
Be output as Y IC = y N + 1 y N + 2 · · · y N + k , So the extreme learning machine mapping matrix that is formed by newly arrived sample data is:
H ( X IC ) = G ( a 1 , b 1 , x N + 1 ) G ( a 2 , b 2 , x N + 1 ) · · · G ( a L , b L , x N + 1 ) G ( a 1 , b 1 , x N + 2 ) G ( a 2 , b 2 , x N + 2 ) · · · G ( a L , b L , x N + 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N + k ) G ( a 2 , b 2 , x N + k ) · · · G ( a L , b L , x N + k )
T+1 is extreme learning machine weighting parameter W constantly t+1Upgrade in the following manner:
W t+1＝K tW t+K tA t -1H(X IC) TY IC
Wherein:
K t＝I-A t -1H(X IC) T[H(X IC)A t -1H(X IC) T+I k×k] -1H(X IC)
A t - 1 = [ 1 v + H ( X t ) T H ( X t ) ] - 1
A t+1 -1＝K tA t -1
I K * kIt is 1 unit matrix for diagonal line;
K t, A t -1Be the intermediate variable of introducing, upgrade rear weighting parameter W thereby simplify t+1Expression-form;
Step (4): training process stops
After all training datas all participated in training, training process stopped, the extreme learning machine weighting parameter W after this moment, the output training was completed;
Step (5): the online application
Suppose that the test sample book quantity that need to carry out the lithographic line width prediction is N Test, train the extreme learning machine model parameter W that obtains, carry out according to the following formula the intelligent predicting of lithographic line width:
Y ^ test = H ( X test ) W
X wherein TestBe input corresponding to sample to be predicted, Be the predicted value of photoetching district live width, H (X Test) expression-form is as follows:
H ( X test ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N test ) G ( a 2 , b 2 , x N test ) · · · G ( a L , b L , x N test ) .
Description of drawings
Fig. 1: algorithm flow chart is each performing step of the lithographic line width prediction algorithm that proposes of the present invention;
Fig. 2: the measuring accuracy of lithographic line width data, after utilizing actual lithographic line width data to carry out modeling, utilize the model after training that live width is predicted the outcome;
Fig. 3: this algorithm is needed software and hardware composition diagram in enterprise's use procedure.
Embodiment
The present invention proposes the lithographic line width Intelligent Forecasting based on dimensionality reduction and increment type extreme learning machine, its main advantage is that precision of prediction is high, adopt simultaneously the on-line study method, the characteristics that in batches arrive to adapt to data, in actual application, if when having new data to arrive, just carry out at once model learning, and the model parameter that upgrades in time; If when arriving without new data, utilize the model of having trained to predict.On-line study method of the present invention depends on the hardware devices such as relevant data acquisition system (DAS), arithmetic server and subscription client, and is realized by the intelligent predicting software based on the lithographic line width Intelligent Forecasting of the conversion of matrix inversion dimensionality reduction and increment type extreme learning machine.
Step (1): gather the historical data information of litho machine, the correlation parameter information of processing lot:
The initialization information that gathers comprises processing menu, gluing thickness, exposure dose, gluing quality control value, the quality control value of exposure dose of photoetching machine, live width standard, historical measurements, the focal length of photoetching machine of lot, and initialization information is stored in database;
Step (2): Model Selection
To the method that the present invention proposes, Model Selection relates generally to the selection of the number of hidden nodes L.For the number of hidden nodes, according to the approximation theory of extreme learning machine algorithm, as long as the number of hidden nodes is enough large, algorithm can approach function arbitrarily with arbitrary accuracy, so in the present invention, the number of hidden nodes is chosen a relatively large value and got final product, and is taken as L=100.
Step (3): the model preset parameter arranges
The initialization of model is mainly that all parameters of model that relate in algorithm are determined value.In invention, the value of model parameter comprises the parameter a of radial basis function i, b i, initialization sample is counted N 0, penalty factor v selects.a i, b iBe the parameter of radial basis function, a iDimension is 29 dimensions, and it can be chosen from [11] at random, b iBe 1 the dimension, value be from 1 100 13 300 Choose at random; Initialization sample is counted N 0=L+200, L are given the number of hidden nodes, L=100.For the selection of penalty factor v, can be { 2 -24, 2 -23..., 2 24, 2 25Select in scope, the experience value is 2 -15
Step (4): algorithm initialization
For moment t, the weighting parameter W of increment type extreme learning machine tInitialization value is:
W t = [ 1 v + H ( X t ) T H ( X t ) ] - 1 H ( X t ) T Y t
Wherein:
X tThe sample that expression t has obtained constantly, sample size is N, so the extreme learning machine mapping matrix that produces is:
H ( X t ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N ) G ( a 2 , b 2 , x N ) · · · G ( a L , b L , x N )
Y t = y 1 y 2 · · · y N
Step (5): on-line study process
For t+1 constantly, the quantity of supposing new arrival sample is k, newly arrives corresponding being input as of sample
Figure BSA00000823698800054
Be output as Y IC = y N + 1 y N + 2 · · · y N + k , So the extreme learning machine mapping matrix that is formed by newly arrived sample data is:
H ( X IC ) = G ( a 1 , b 1 , x N + 1 ) G ( a 2 , b 2 , x N + 1 ) · · · G ( a L , b L , x N + 1 ) G ( a 1 , b 1 , x N + 2 ) G ( a 2 , b 2 , x N + 2 ) · · · G ( a L , b L , x N + 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N + k ) G ( a 2 , b 2 , x N + k ) · · · G ( a L , b L , x N + k )
T+1 is extreme learning machine weighting parameter W constantly t+1Upgrade in the following manner:
W t+1＝K tW t+K tA t -1H(X IC) TY IC
Wherein:
K t＝I-A t -1H(X IC) T[H(X IC)A t -1H(X IC) T+I k×k] -1H(X IC)
A t - 1 = [ 1 v + H ( X t ) T H ( X t ) ] - 1
A t+1 -1＝K tA t -1
I K * kIt is 1 unit matrix for diagonal line;
K t, A t -1Be the intermediate variable of introducing, upgrade rear weighting parameter W thereby simplify t+1Expression-form;
Step (6): training process stops
After all training datas all participated in training, training process stopped, the extreme learning machine weighting parameter W after this moment, the output training was completed;
Step (7): the online application
Suppose that the test sample book quantity that need to carry out the lithographic line width prediction is Nt est, train the extreme learning machine model parameter W that obtains, carry out according to the following formula the intelligent predicting of lithographic line width:
Y ^ test = H ( X test ) W
X wherein TestBe input corresponding to sample to be predicted,
Figure BSA00000823698800062
Be the predicted value of photoetching district live width, H (X Test) expression-form is as follows:
H ( X test ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N test ) G ( a 2 , b 2 , x N test ) · · · G ( a L , b L , x N test ) .
Put forward the methods process flow diagram of the present invention as shown in Figure 1.
Based on the above-mentioned line modeling method that proposes, the present invention has done a large amount of l-G simulation tests, because length is limit, only provides this invention here and is applied to actual effect in the lithographic line width forecasting process.Data inputs is comprised of 29 dimension data, is mainly the quality control value, wire width measuring value and the photoresist thickness that are in exposure dose corresponding to front 5 lot of identical processing level, same breed, focal length of photoetching machine, exposure dose with lot to be predicted; And quality control value and the photoresist thickness of the exposure dose of current lot to be predicted, focal length of photoetching machine, exposure dose.Data are taken from the industry spot data between 2012-2-9 to 2012-7-16, and totally 2250, arbitrarily choose wherein 1000 as test data, remaining 1250 as training data.
The correlation parameter value is as shown in the table.
Table 1 parameter value table
Figure BSA00000823698800064
The present invention and on-line Algorithm OS-ELM preferably (online order limit learning machine) and Fixed-LSSVM (fixed size least square method supporting vector machine) compare, and comparative result is as shown in table 2
Table 2LS-IELM and OS-ELM, Fixed-LSSVM algorithm performance comparative result
Figure BSA00000823698800071
As can be seen from the table, the on-line Algorithm that the present invention proposes is compared OS-ELM, Fixed-LSSVM and is had better measuring accuracy, therefore has better generalization ability.
Fig. 2 has provided the graph of errors between all test data predicted values and actual value, can see that all predicated errors all between [0.1,0.1], satisfy the regulating scope requirement of actual lithographic line width.

Claims (1)

1. based on the lithographic line width Intelligent Forecasting of dimensionality reduction and increment type extreme learning machine, it is characterized in that, described method is to realize according to the following steps successively on computers:
Step (1): Model Selection and parameter initialization
For a given N sample, its input is designated as
Figure FSA00000823698700011
X wherein iRepresent every i sample, by the vector that 29 dimension data form, this vector comprises following parameter: be in quality control value, wire width measuring value and the photoresist thickness of exposure dose corresponding to front 5 lot of identical processing level, same breed, focal length of photoetching machine, exposure dose with lot to be predicted; The quality control value of the exposure dose of current lot to be predicted, focal length of photoetching machine, exposure dose and photoresist thickness; N the corresponding output of sample input is designated as
Figure FSA00000823698700012
y iBe the lithographic line width measured value;
The number of hidden nodes L of given extreme learning machine based on structural risk minimization adopts radial basis function as the eigentransformation function, and functional form is G ( a i , b i , x i ) = e - b i ( | | x i - a i | | ) , i = 1,2 , · · · , L , A wherein i, b iBe the parameter of radial basis function, a iDimension is 29 dimensions, and it can be chosen from [1 1] at random, b iBe 1 the dimension, value be from 1 100 13 300 Choose at random;
So the extreme learning machine Feature Mapping matrix H (X) of generation is:
H ( X ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N ) G ( a 2 , b 2 , x N ) · · · G ( a L , b L , x N )
Step (2): algorithm initialization
For moment t, the weighting parameter W of increment type extreme learning machine tInitialization value is:
W t = [ 1 v + H ( X t ) T H ( X t ) ] - 1 H ( X t ) T Y t
Wherein:
X tThe sample that expression t has obtained constantly, sample size is N, so the extreme learning machine mapping matrix that produces is:
H ( X t ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N ) G ( a 2 , b 2 , x N ) · · · G ( a L , b L , x N )
Y t = y 1 y 2 · · · y N
V adopts empirical value for the compromise coefficient, is taken as 2 -15
Step (3): on-line study process
For t+1 constantly, the quantity of supposing new arrival sample is k, newly arrives corresponding being input as of sample
Figure FSA00000823698700021
Be output as Y IC = y N + 1 y N + 2 · · · y N + k , So the extreme learning machine mapping matrix that is formed by newly arrived sample data is:
H ( X IC ) = G ( a 1 , b 1 , x N + 1 ) G ( a 2 , b 2 , x N + 1 ) · · · G ( a L , b L , x N + 1 ) G ( a 1 , b 1 , x N + 2 ) G ( a 2 , b 2 , x N + 2 ) · · · G ( a L , b L , x N + 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N + k ) G ( a 2 , b 2 , x N + k ) · · · G ( a L , b L , x N + k )
T+1 is extreme learning machine weighting parameter W constantly t+1Upgrade in the following manner:
W t+1＝K tW t+K tA t -1H(X IC) TY IC
Wherein:
K t＝I-A t -1H(X IC) T[H(X IC)A t -1H(X IC) T+I k×k] -1H(X IC)
A t - 1 = [ 1 v + H ( X t ) T H ( X t ) ] - 1
A t+1 -1＝K tA t -1
I K * kIt is 1 unit matrix for diagonal line;
K t, A t -1Be the intermediate variable of introducing, upgrade rear weighting parameter W thereby simplify t+1Expression-form;
Step (4): training process stops
After all training datas all participated in training, training process stopped, the extreme learning machine weighting parameter W after this moment, the output training was completed;
Step (5): the online application
Suppose that the test sample book quantity that need to carry out the lithographic line width prediction is N Test, train the extreme learning machine model parameter W that obtains, carry out according to the following formula the intelligent predicting of lithographic line width:
Y ^ test = H ( X test ) W
X wherein TestBe input corresponding to sample to be predicted, Be the predicted value of photoetching district live width, H (X Test) expression-form is as follows:
H ( X test ) = G ( a 1 , b 1 , x 1 ) G ( a 2 , b 2 , x 1 ) · · · G ( a L , b L , x 1 ) G ( a 1 , b 1 , x 2 ) G ( a 2 , b 2 , x 2 ) · · · G ( a L , b L , x 2 ) · · · · · · · · · · · · G ( a 1 , b 1 , x N test ) G ( a 2 , b 2 , x N test ) · · · G ( a L , b L , x N test ) .
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CN104503420A (en) * 2014-09-19 2015-04-08 北京化工大学 Non-linear process industry fault prediction method based on novel FDE-ELM and EFSM
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CN107423547A (en) * 2017-04-19 2017-12-01 江南大学 Increment type location algorithm based on the semi-supervised learning machine that transfinites
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