CN107560556A - The method of white light reflectance measurement film thickness based on L M optimized algorithms - Google Patents
The method of white light reflectance measurement film thickness based on L M optimized algorithms Download PDFInfo
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Abstract
The invention discloses a kind of method of the white light reflectance measurement film thickness based on L M optimized algorithms.This method will be using the BP neural network of L M optimized algorithms to carrying out study fitting by the signal of noise pollution in dynamic measurement, WLRS curves after being fitted, the thickness of film to be measured is rapidly and accurately measured by the characteristic value for obtaining the WLRS curves after being fitted, proves that this method has stronger antijamming capability and certain adaptability by actual measure.
Description
Technical field
The invention belongs to optical precision measurement and field of signal processing, and in particular to a kind of based on the white of L-M optimized algorithms
The method that light reflectivity measures film thickness.
Background technology
It is well known that if semiconductor devices is processed using the semiconductor technology of higher precision, by chip
Electric property is such as：The characteristics such as power consumption, frequency response are obviously improved effect.And high-acruracy survey is then lifting machining accuracy
A not retrievable ring.White light reflectance spectrum (White Light Reflectance Spectroscopy, WLRS) technology
Measurement model is as shown in Figure of description 1.Its cardinal principle is in dielectric surface S from the white light that white light emitter is launched1、S2
Constantly refraction reflection so that light phase changes.Can by analyze calculate phase place change obtain one group of reflectivity with
Relation curve between wavelength, the curve are exactly WLRS curves.
During actual processing, often because of various reasons such as：Crystal impurity concentration, inevitable noise
Deng causing the curve measured by measured curve and laboratory ecotopia to have larger gap.What accompanying drawing 2 represented is exactly different
The film of purity WLRS static measurement curves resulting under same thickness (thickness 210.4nm), it can be seen that have certain
The film of the impurity of amount is because refractive index and theoretical refractive index have larger difference, so static measurement values have larger difference.When
So, the influence in the WLRS curves in the case that dynamic measures caused by noise will be bigger.
The present invention will use BP (Back-Propagation) god of L-M (Levenberg-Marquardt) optimized algorithm
Through network model, to being fitted by the dynamic WLRS signals of noise pollution, utilized finally by the mode of prediction after being fitted
Neural network model obtains complete WLRS signals, obtains its characteristic value and film thickness is effectively judged.
The content of the invention
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of white light reflection based on L-M optimized algorithms
Rate measures film thickness adaptive approach, solves problems with：
1) dynamic measuring data contains the problem of larger noise；
2) the less problem of dynamic measuring data amount；
3) the problem of how WLRS curves obtain film thickness to be measured.
The technical solution adopted in the present invention, comprise the following steps：
1) launch white light from air to film to be measured using white light emitter, refraction reflected light is obtained in signal acquisition region
Line obtains one group of original WLRS signal.
2) training set, setting training time are introduced after one group of original WLRS signal obtained by step 1 is normalized
Number, training objective error.
3) L-M Optimized BP Neural Network training is carried out using to the data in the training set obtained by step 2, it is determined that prediction mould
The hidden layer number of plies, each node in hidden layer, hidden layer transfer function and the output layer transfer function of type.
4) emulation is predicted to the WLRS models of training gained, the WLRS curves after being fitted.
5) to the WLRS curve acquisition characteristic values after fitting, the film thickness corresponding to the curve is judged by characteristic value.
The advantage of the invention is that：
1) noise signal during dynamic measures is effective filtered out；
2) less measurement data is used, reduces the time used in measurement；
3) relation between WLRS curves and film thickness is established by characteristic value, increases systematic survey speed；
4) model is adaptively established, has certain adaptability to the silicon wafer fenestra containing certain impurity, reduces to material purity
Dependence, make system that there is certain adaptability.
Brief description of the drawings
Fig. 1 is WLRS signal pickup assembly structure charts；
Fig. 2 be different purity film under same thickness WLRS static measurements curve map；
Fig. 3 is the BP neural network structure chart of L-M optimized algorithms；
Fig. 4 is implementation process figure of the present invention；
Fig. 5 is the matched curve of L-M algorithms, static measurement curve, the contaminated curve comparison figure of dynamic；
Fig. 6 is the curve after fitting, curve and equal thickness high purity films eigenvalue of curve comparison diagram before fitting.
Embodiment
Below, this method will be explained with reference to accompanying drawing.
1) launch white light from air to film to be measured using white light emitter, refraction reflected light is obtained in signal acquisition region
Line obtains one group of original WLRS signal；
Specially：As shown in Figure 1, beam of white light A by white light emitter with incident angle α from air directive film to be measured,
Wherein incident angle α is less than ± 5 °.Light is in upper and lower interface S1、S2Refraction reflection is repeated, finally will in signal acquisition region
Light B after refraction reflection repeatedly1、B2、…、Bn, by the phase difference of the light collected, draw one group of original WLRS signal.
2) training set, setting training time are introduced after one group of original WLRS signal obtained by step 1 is normalized
Number, training objective error；
Specially：Original WLRS signals generally are the data between 0-1, but due to may caused by noise jamming and
Other reasonses may make the WLRS signals obtained by calculating excessive or too small, and in order to prevent the above situation, WLRS is returned
One change is handled, and its formula is：
Wherein, S*For the WLRS signal datas after normalization, S is WLRS primary signals, SmaxAnd SminRespectively WLRS is former
Maximum and minimum value in beginning signal data.
It is 1000 to set frequency of training, and training objective error is 0.001, when neural metwork training number reaches frequency of training
Or when the error after training is less than training objective error with regard to deconditioning, the forecast model after output training.
3) L-M Optimized BP Neural Network training is carried out using to the data in the training set obtained by step 2, it is determined that prediction mould
The hidden layer number of plies, each node in hidden layer, hidden layer transfer function and the output layer transfer function of type；
Specially：Because application involved in the present invention is nonlinear system, therefore use L-M algorithm amendment BP neural networks
Weights, its specific formula are：
Δ ω=(JT+μI)-1JTe (2)
Wherein, e represents error vector of the neutral net for several times after iteration, and e specific formula is：
E=[e1,e2,...,en]T (3)
Wherein e1、e2、…enRespectively BP neural network the 1st time, the 2nd time ..., the error of nth iteration.
J represents error eiTo neural network weight ωiThe Jacobian matrix of differential, wherein i=1,2 ..., n, represent nerve
The iterations of network.
J can specifically be tried to achieve by equation below：
μ is the positive integer of a value very little, and I is unit matrix.
In application involved in the present invention, it is 1 layer generally to set the implicit number of plies, in actual applications also can be according to reality
Need necessarily to adjust the hidden layer number of plies.
Node in hidden layer is set according to data volume situation, in order to reach flat between pace of learning and simulation data error
Weighing apparatus, node in hidden layer is typically arranged to 5 for application of the present invention, also can be according to being actually needed to hidden layer section
Points are necessarily adjusted.
The hidden layer transfer function for setting forecast model is logsig functions, and its specific formula is：
Wherein, y is the output of hidden layer transfer function, and x is the input of hidden layer transfer function.
The output layer transfer function for setting forecast model is purelin functions, and its specific formula is：
Y=x (6)
Wherein, y is the output of output layer transfer function, and x is the input of output layer transfer function.
The BP neural network structure chart of L-M optimized algorithms is as shown in Figure 3.
4) emulation is predicted to the WLRS models of training gained, the WLRS curves after being fitted；
Specially：Because the WLRS models obtained by step 3 are to be trained study by the curve after normalizing, so output
Also should be the matched curve after normalization, so renormalization processing need to be done to curve.But due to WLRS curve reflectivity
The general all boundaries of value between 0 and 1, acquired characteristic value is unrelated with WLRS curve actual sizes in step 5, it is merely meant that phase
To magnitude relationship, therefore neutral net can be fitted to prediction curve directly as final curves.
5) to the WLRS curve acquisition characteristic values after fitting, the film thickness corresponding to the curve is judged by characteristic value.
Specially：WLRS curves after fitting are considered as the WLRS curves obtained by actual film thickness, after fitting
Optical wavelength corresponding to the minimum point of WLRS curves is set to characteristic value, and characteristic value is closed with film thickness to be measured there is linear
System, the thickness of film to be measured can be quickly obtained by this feature value.
Implementation process figure of the present invention as shown in Figure 4, present invention will be further expalined by example below,
Here exemplified by film thickness will be used as 210.4nm WLRS.Silicon single crystal wafer is by environment power frequency in being measured due to live reality
There is some difference etc. that reason, original WLRS signals are disappeared by noise for noise, tested film purity, and curve has larger hair
Thorn, as dynamically measured in accompanying drawing 5 shown in white light reflectance spectrum, what is represented in accompanying drawing 5 is specific contaminated WLRS Dynamic Signals
When film thickness to be measured is all 210.4nm, by noise when the matched curve of L-M algorithms, static measurement curve and dynamic measure
The contrast effect of interference curve.Wherein, algorithm matched curve is represented that static measurement WLRS curves are illustrated by the broken lines by solid line, and
Dynamically contaminated curve is then represented by.The primitive curve that step 1 of the present invention is obtained is that dynamically measurement is got dirty in accompanying drawing 5
Shown in the curve of dye, it can be seen that though by influence of noise, dynamic measure the still middle numerical value of WLRS curves be still within 0-1 it
Between, but for the ease of calculating and uniformly, therefore still performance graph is normalized.Curve after normalization is subjected to L-
M neural metwork trainings, set：
1) it is 1 to imply the number of plies；
2) node in hidden layer is 5；
3) hidden layer transfer function is logsig functions；
4) output layer transfer function is purelin functions；
5) frequency of training 1000；
6) training objective error is 0.001.
WLRS models are drawn after training, WLRS is emulated, obtain the WLRS curves after the fitting of L-M algorithms, it is specific bent
Line is shown in L-M algorithms matched curve in accompanying drawing 5, and digital simulation root-mean-square error (Mean Squared Error, MSE) is
0.0097, formula is：
Wherein TiFor static measurement data, Y corresponding to every group of WLRS curveiTo be fitted output data, N is fitting gained
Output data is counted.
Still there is certain burr by the visible algorithm matched curve of accompanying drawing 5, and static measurement data are then relatively smooth, but by
It is the wavelength corresponding to minimum point in characteristic value, the fluctuation of small range, therefore can be with to asking for the result difference of characteristic value and little
Ignore the small range fluctuation of matched curve.
Matched curve characteristic value finally is asked for, single-point feature value does not possess persuasive ability, so multiple points will be taken to algorithm
Quality is analyzed.As shown in Figure 6, the eigenvalue of curve in the range of certain film thickness after (200-250nm) fitting with
The contrast of eigenvalue of curve before fitting, it can intuitively find out after being fitted there is obvious linear relationship before curve comparison fitting.When
Only it is merely so that observation directly perceived can not illustrate whole issue, here by using root-mean-square error (the Root Mean with fitting a straight line
Square Error, RMSE) analyze the linear degrees of three curves as index quantification, its formula is：
Wherein Xobs,iWith Xmodel,iRespectively observation and theoretical true value.It is attached in this example, observation is three in figure
The actual characteristic value of curve, and theoretical true value is then to pass through the characteristic value corresponding to the straight line of least square fitting.N is sample
Point quantity.
It can be calculated by formula 8, the higher crystal characteristic value of dynamic experiment curv, the matched curve of L-M algorithms, purity is bent
The RMSE of line is respectively 102.8831,24.5156,7.881.It can be seen that the linear degree of L-M algorithms and the higher crystal of purity
Static measurement curve is compared also there is a certain distance, but compared to the result of dynamic experiment curv, is then had larger
Improve.It can be found that the eigenvalue graph after L-M algorithms relatively connects with dynamic experiment curv in height by Fig. 6 simultaneously
Closely, this be due to the purity of crystal it is inadequate caused by, illustrate that L-M algorithms have certain adaptability.Can be with by above-mentioned result
Illustrate that the present invention has preferable effect.
Claims (5)
1. the method for the white light reflectance measurement film thickness based on L-M optimized algorithms, it is characterised in that comprise the following steps：
1) launch white light from air to film to be measured using white light emitter, refraction reflection light is obtained in signal acquisition region and is obtained
To one group of original WLRS signal；
2) training set, setting frequency of training, instruction are introduced after one group of original WLRS signal obtained by step 1 is normalized
Practice target error；
3) L-M Optimized BP Neural Network training is carried out using to the data in the training set obtained by step 2, determines forecast model
The hidden layer number of plies, each node in hidden layer, hidden layer transfer function and output layer transfer function；
4) emulation is predicted to the WLRS models of training gained, the WLRS curves after being fitted；
5) to the WLRS curve acquisition characteristic values after fitting, the film thickness corresponding to the curve is judged by characteristic value.
2. the method for the white light reflectance measurement film thickness according to claim 1 based on L-M optimized algorithms, its feature
It is that the step 1 is specially：Beam of white light A by white light emitter with incident angle α from air directive film to be measured, wherein incident
Angle α is less than ± 5 °；Light is in upper and lower interface S1、S2Refraction reflection is repeated, will finally be reflected repeatedly in signal acquisition region
Light B after reflection1、B2、…、Bn, by the phase difference of the light collected, draw one group of original WLRS signal.
3. the method for the white light reflectance measurement film thickness according to claim 1 based on L-M optimized algorithms, its feature
It is that the step 2 is specially：WLRS is normalized, its formula is：
<mrow>
<msup>
<mi>S</mi>
<mo>*</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mi>S</mi>
<mo>-</mo>
<msub>
<mi>S</mi>
<mi>min</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mi>min</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, S*For the WLRS signal datas after normalization, S is WLRS primary signals, SmaxAnd SminRespectively WLRS primary signals
Maximum and minimum value in data；
It is 1000 to set frequency of training, and training objective error is 0.001, when neural metwork training number reaches frequency of training or works as
With regard to deconditioning when error after training is less than training objective error, the forecast model after output training.
4. the method for the white light reflectance measurement film thickness according to claim 1 based on L-M optimized algorithms, its feature
It is that the step 3 is specially：Using L-M algorithm amendment BP neural network weights, its specific formula is：
Δ ω=(JT+μI)-1JTe (2)
Wherein, e represents error vector of the neutral net for several times after iteration, and e specific formula is：
E=[e1,e2,...,en]T (3)
Wherein e1、e2、…enRespectively BP neural network the 1st time, the 2nd time ..., the error of nth iteration；
J represents error eiTo weights ωiThe Jacobian matrix of differential, wherein i=1,2 ..., n, represent that the iteration of neutral net is secondary
Number；
J is specifically tried to achieve by equation below：
μ is the positive integer of a value very little, and I is unit matrix；
It is 1 layer to set the implicit number of plies, and node in hidden layer is arranged to 5；
The hidden layer transfer function for setting forecast model is logsig functions, and its specific formula is：
<mrow>
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, y is the output of hidden layer transfer function, and x is the input of hidden layer transfer function；
The output layer transfer function for setting forecast model is purelin functions, and its specific formula is：
Y=x (6)
Wherein, y is the output of output layer transfer function, and x is the input of output layer transfer function.
5. the method for the white light reflectance measurement film thickness according to claim 1 based on L-M optimized algorithms, its feature
It is that the step 5 is specially：WLRS curves after fitting are considered as the WLRS curves obtained by actual film thickness, after fitting
WLRS curves minimum point corresponding to optical wavelength be set to characteristic value, characteristic value is closed with film thickness to be measured there is linear
System, the thickness of film to be measured is quickly obtained by this feature value.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0011723A1 (en) * | 1978-12-04 | 1980-06-11 | International Business Machines Corporation | Process and device for the interferometric measurement of changing film thicknesses |
| CN102735176A (en) * | 2012-06-25 | 2012-10-17 | 浙江大学 | Device and method for detecting optical film thickness based on optical fiber spectrometer |
| CN105138717A (en) * | 2015-07-09 | 2015-12-09 | 上海电力学院 | Transformer state evaluation method by optimizing neural network with dynamic mutation particle swarm |
-
2017
- 2017-08-17 CN CN201710704879.1A patent/CN107560556A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0011723A1 (en) * | 1978-12-04 | 1980-06-11 | International Business Machines Corporation | Process and device for the interferometric measurement of changing film thicknesses |
| CN102735176A (en) * | 2012-06-25 | 2012-10-17 | 浙江大学 | Device and method for detecting optical film thickness based on optical fiber spectrometer |
| CN105138717A (en) * | 2015-07-09 | 2015-12-09 | 上海电力学院 | Transformer state evaluation method by optimizing neural network with dynamic mutation particle swarm |
Non-Patent Citations (6)
| Title |
|---|
| 刘滢滢 等: "《白光反射谱测薄膜厚度实验》", 《仪器仪表标准化与计量》 * |
| 吴百诗: "《大学物理（第三次修订本）下册》", 30 October 2008, 西安交通大学出版社 * |
| 康惠蓉: "《大学物理》", 31 August 2013, 云南科技出版社 * |
| 曲云霞 等: "《基于BP 神经网络的噪声背景下的信号识别》", 《机械设计》 * |
| 赵仁宏 等: "《医用物理学》", 31 May 2010, 山东人民出版社 * |
| 赵近芳 等: "《大学物理学》", 31 January 2016, 北京邮电大学出版社 * |
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Application publication date: 20180109 |