CN109060860A - A kind of comparative approach and device of SIMS analysis curve - Google Patents
A kind of comparative approach and device of SIMS analysis curve Download PDFInfo
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Abstract
The present invention provides the comparative approach and device of a kind of SIMS analysis curve, for diagnosing ion implanting with the presence or absence of abnormal, comprising the following steps: S1 finely tunes board；S2, the first decision phase, board carries out the self checking of ion implantation dosage deviation, if ion implantation dosage deviation less than 1%, goes to step S3, if ion implantation dosage difference is more than or equal to 1%, goes to step S1；S3 carries out outlier detection and rejects；S4 carries out curve smoothing processing and carries out Model Diagnosis；S5 calculates relevant nonparametric quantizating index and carries out the comparison of SIMS analysis curve according to the index；S6, if the index meets threshold value, secondary ion injection is normal；If being unsatisfactory for threshold value, secondary ion injection is abnormal, goes to step S1.The comparison parameter for solving SIMS analysis curve in the prior art is excessively subjective, and ion implanting result analyzes incomplete problem, effective to realize early detection and practitioner is instructed to formulate solution in time, reduces the influence of deviation.
Description
Technical field
The present invention relates to field of semiconductor manufacture, in particular to the comparative approach of a kind of SIMS analysis curve and
Device.
Background technique
Recently as the demand rapid growth to sub-nanometer depth resolution and higher sensitivity, Secondary Ion Mass Spectrometry
Analysis (SMIS) receives more and more attention.SIMS bombards sample surfaces by the primary ions beam of high-energy, makes sample
Surface absorption energy and generate secondary ion, by mass analyzer mobile phone, analyze these secondary ions, so that it may obtain about
The map of sample surface information.Compared to other surfaces analytical technology, such as scanning electron microscopy (SEM, Scanning
Electron Microscopy), energy dispersive spectrum (EDS, Energy Dispersive Spectroscopy), electronics energy of having a rest
Compose (AES, Auger Electron Spectroscopy) and x-ray photoelectron spectroscopy (XPS, X-ray Photoelectron
Spectroscopy), sensitivity is very high, from hundred a ten thousandths (PPM) to part per billion (PPB).In addition to this, SIMS is also
With some special advantages, especially in depth and imaging resolution.These functions can be achieved on the institute including hydrogen
There are Element and isotope, analysis of compounds component and molecular structure, however these cannot be detected by SEM and XPS.Fig. 1
It is a SIMS operation principle schematic diagram.Leading ion beam energy range is bombarded sample surfaces in 250eV to 30K eV and is produced
The secondary ion of raw ionization, these subsequent secondary ions are by electric field acceleration and by spectrometer analysis.
For reliability assessment and semiconductor technology control, the quantitative analysis of impurity is most important.It is commented from reliability
From the perspective of estimating, accurate SIMS profile analysis with compare it is consistent most important for ensuring reliability performance, such as new
Equipment is let pass in process transfer, and enough redundancies are most important.Earlier evaluations believable for these occasions depend on SIMS
The robust analysis of depth curve (SDP, SIMS depth profiles) and compare.If in ion implanting (IMP, ion
Implantation it not can recognize that underproof SDP after), need the wafer acceptance testing of equal till all hours (may be after one month)
(WAT, Wafer Acceptance Test) and/or subsequent chip detection (CP, Chip Probing)/final test (FT,
Final Test) detect these negative effects.It will be apparent that until reliability test just detects that rejected product is suitable
Bad.On the other hand from the point of view of, this also means that on line (inline), the performance of WAT, CP, FT and reliability can be comprehensively anti-
Reflect SDP performance and it is necessary to SDP benchmark is further verified and optimized by these results.
From the perspective of semiconductor technology control, SIMS plays an important role in surface analysis, for example, supporting technique
Exploitation, monitoring and troubleshooting.In microelectronic field, what sample was generally flat, and substance is usually low-density, only
It can be arrived by what SIMS was detected.Device formed be from wafer IMP or dopant be diffused into the specific pattern limited by mask
Start.SIMS can determine junction depth by obtaining with the dopant profile of the dopant atom density matching of substrate, this is right
It is even more important in current an ultra shallow implant devices junction depth (< 10nm).In above-mentioned all applications, it is based on ion dose and distribution,
SDP is compared with theoretical or benchmark the section for judgement.
For the SDP in Fig. 2, " Y " axis indicates that concentration (usually being indicated with logarithmic scale) and " X " axis indicate depth, energy
It is intuitive to reflect ion concentration with the situation of change of sample depth, so when ion implantation apparatus implants ions into control wafer
(Split) in, then pass through while analyzing and comparing control wafer and standard sample (BL).There is known depth, dense by IMP creation
The standard of degree or dosage is used for the quantitative calibration to each sample.SIMS develops to dosage measurement skill from semi-quantitative method
Art measures relative standard deviation < 1% with impurity and matrix element for quadrupole rod, magnetic sector and ToF analysis instrument
Reproducibility.
SIMS becomes the mainstream of semicon industry in the application of depth section.In general, the SDP of amorphous layer obeys Gauss point
Cloth is however, there are several different interactions between the ion and crystal column surface of injection.The energy of some ions is sufficiently high,
So that almost all of ion is all injected into wafer；Also it is all reflected by wafer when or energy is very weak.Channelling effect refers to
Ion is parallel to crystallographic axis or planar movement and shows abnormality deep the case where penetrating into crystal lattices.Channelling effect is IMP mistake
It needs to avoid as possible in journey, because it causes the ion of injection out of control and deviates Gaussian Profile.In this case, although it is smart
Energy really is set, but small angle offset can generate significant difference.Fig. 2 discloses two different implant angles,
0 ° and 1 °, SDP there are significant differences.It may be tired in the quantization of interface (shallow depth) and posture (especially deeper depth)
Difficult.In the depth for being less than 200nm, due to disturbance caused caused by pollution, so that the SDP of low mass resolution rate and can not
It leans on.However, in the depth for being greater than 800nm, restriction of the detectivity of SDP by detection boundary.
IMP is a kind of low temperature process that the impurity accurately controlled is introduced to semiconductor, it provides more than diffusion process
Flexibility.Ion implantation apparatus is generally divided into high current (HC, high current), middle electric current (MC, medium current),
High energy (HE, high energy) and low energy (LE, low energy).The typical performance indicators of beam-line ion implanter have
Even property, repeatability, reliability, for the angle in situ control that accurate pure doping is placed, high-throughput and contamination control.Note every time
Entering can be realized by the beam current of control IMP technique, Implantation Energy, angle and dopant, these are all to device
Performance And Reliability is most important.In most cases, ion will be implanted on wafer with certain tilt angle to reduce channel
The influence of effect.Common practice is with the injection of 7 ° of inclination angles to avoid doped channel, although 7 ° are inclined due to the shade of photoresist
It tiltedly may not be best.By utilizing channel, 0 ° of inclination can be used with associated compared with low energy to realize that target is deep
It spends and can be reduced damage for injecting compared to inclination.By taking HE implanter as an example, since cone angle effects batch tool may cause
Difference channel, this may cause the large change of dopant profiles on wafer, inject especially for 0 °.On the other hand, single crystalline substance
Circle HE implanter is not influenced by this cone angle effects, it is possible to provide uniform 0 ° of injection.These characteristics of single wafer implanter
Particularly advantageous for cmos image sensor (CIS) application, these applications need depth to inject, and have to wafer uniformity tightened up
Requirement.In short, the slight shift of angle will generate significant impact to SDP, and implant angle be the key that IMP process because
Element.
In addition to above-mentioned Implantation Energy and angle, the degree that equipment is degenerated also seriously affects SDP.Such as light beam line portion
The abrasion and degeneration divided is so that hardware is gradually distance from original setting.Therefore, the precision of periodic verification implant angle and ion gauge can
To reduce process variation to the maximum extent.Generally use measurement heat wave (TW, thermal-wave) signal and line resistance (Rs,
Sheet resistances) to monitor deviation of the injector angle relative to crystallographic axis.However TW has sensitivity curve, this makes
It is difficult under certain injection conditions.This tool is efficiently used, it is necessary to the calibration table of specific flow setting operation is taken,
Even if the Rs value between two specific ion implanters may also have significant difference under identical implant angle.From theory
On say, any IMP extremely can be by finding SIMS result compared with benchmark.
For a long time, SDP relatively depends on the subjective assessment of practitioner, is not based on times of statistics or physics
What significant index.As shown in Figure 2,1 ° of angle difference leads to significant different SDP.Further in fig. 3 a, according to working
The comment of person has, and the SDP of the sample (" Split ") for identification is matched well with reference sample (" Baseline ").In Fig. 3 b
In, the IMP doses change of sample to be identified is in limitation range, but SDP matching is than the difference in Fig. 3 a；In this case, very
Hardly possible judges whether the SDP in Fig. 3 b is subjected to.In Fig. 2, sample to be tested (" Split ") and reference sample (" Baseline ")
There are significant differences between SDP.Therefore, only according to vision can relatively easily from the SDP identification in Fig. 2, there are ion implantation apparatuses
It is abnormal.
Just because of this, it is obviously desirable to one can quantify and have more meaningful index to compare SDP.In order to obtain a ratio
Relatively reliable compared with two or more SDP and accurate judgement, forefathers have taken very big effort.Document [1]
(CN104237279A) a kind of judgment method of calculating bias ratio is proposed to compare SDP.It is reduced using Gaussian smoothing method
Signal-to-noise ratio (S/N, Signal-to-Noise), then carries out point-to-point normalization, as shown in Figure 4.
Then this method excludes noise region, and remaining area is divided into one dividing into three, calculates separately respective slope.Most
Afterwards, bias ratio is appointed as by maximum in the absolute value of these slopes.Although being bluntly that there are one for it away from rate method
A little doubts, it is too subjective in some parameter settings.It is described in detail below:
(1) curve smoothing is quite important and basis of subsequent analysis.However, lacking in rate method to curve smoothing
Thoroughly verifying or even exceptional value all do not exclude.Subsequent normalized curve inevitably moves up and down, especially shallower
Deeper depth.
(2) due to not yet accurately obtaining the function of SDP, so-called point-to-point return must be selected away from the author of rate method
One changes.But it depends on the sample frequency of SDP, many information can lose.
(3) acquisition is subjective and unscientific away from the process of rate score.On the one hand, normalized curve not necessarily meets
Linear function.In addition, if two SDP are parallel and there are significant differences, then do not work away from rate method.
(4), actually also should be different away from rate threshold values for a variety of different technology platforms, rather than fixed value,
1.4。
(5) number that acceptable area is divided into several sections is also a lack of theories integration.In addition to this, for zone of acceptability
The identification (effective dose of covering 95%) in domain is also required to further thoroughly discuss.
It (6) is finally also most of all, practical experience shows that deviating from rate method may draw the wrong conclusion, for example, figure
SDP in 3b deviates from rate=1.35 < 1.4. that is, by being considered comparing favourably with Baseline away from the rate method SDP
(because it deviates from rate < 1.4).However, the device (SDP in Fig. 3 b) from the split by hot carrier in jection (HCI,
Hot carrier injection) reliability assessment, as shown in Figure 5.Its Idsat (leakage current when saturation) degenerates obvious
Much larger than Baseline sample.HCI robustness significantly by drain depletion region electric field and channel current distribution influenced,
And these are greatly influenced by ion implantation dosage and angle.
Summary of the invention
The purpose of the present invention is to provide the comparative approach and device of a kind of SIMS analysis curve, for diagnosing
Ion implanting whether there is exception, excessively subjective with the comparison parameter for solving SIMS analysis curve in the prior art,
Ion implanting result analyzes incomplete problem, effective to realize early detection and practitioner is instructed to formulate solution party in time
Case reduces the influence of deviation.
The present invention provides a kind of comparative approach of SIMS analysis curve, whether there is for diagnosing ion implanting
It is abnormal, comprising the following steps:
S1 finely tunes board；
S2, the first decision phase, board carries out the self checking of ion implantation dosage deviation, if ion implantation dosage deviation is less than
1%, then step S3 is gone to, if ion implantation dosage difference is more than or equal to 1%, goes to step S1；
S3 carries out outlier detection and rejects；
S4 carries out curve smoothing processing and carries out Model Diagnosis；
S5 calculates relevant nonparametric quantizating index and carries out the ratio of SIMS analysis curve according to the index
Compared with；
S6, if the index meets threshold value, secondary ion injection is normal；If being unsatisfactory for threshold value, secondary ion injection
It is abnormal, go to step S1.
Optionally, the nonparametric quantizating index is " difference percentage D ", its calculation formula isWhereinGA(x) and GBIt (x) is two given SDP curve smoothings
Function, a represent shallow area's depth value, and b represents deep area depth value.
Optionally, the threshold definitions are 0.276%, i.e., as D≤0.276%, the sample to be tested and standard sample
SDP curve be it is analogous, this time inject normal, work as D > 0.276%, the sample to be tested and standard sample SDP curve exist
Significant difference, it this time injects abnormal.
Optionally, the nonparametric quantizating index be Ke Ermo can love-Si meter love K-S statistic DKS, formula is
DKS=max | F (x)-G (x) |, wherein F (x) and G (x) represents the empirical cumulative distribution function of two SDP curves.
Optionally, the method is not limited by sample distribution and population sample amount size；When the sample dimension is greater than 1
When, it can be in the maximum between the empirical cumulative distribution function described in All Quardrants for finding the sample under any possible sequence
Antipode.
Optionally, when the dimension of the sample is 2, n sample point is provided in two-dimensional space, is calculated by all right
The 4n for the plane that (Xi, Yj) is defined2Empirical cumulative distribution function in quadrant, and calculate the empirical distribution function in All Quardrants
Between maximum antipode, wherein Xi and Yj is the coordinate of any point pair in given sample, and counting step can pass through violence
Algorithm executes, and whether wherein which determines the point to the inswept each quadrant of each point in the sample.
Optionally, if significance a=0.05, the threshold definitions are 0.09, i.e., as DKS≤0.09, institute
State sample to be tested and standard sample SDP curve be it is analogous, this time ion implanting it is normal；Work as D > 0.09, the sample to be tested
It is that there are significant differences with standard sample SDP curve, this time injects abnormal.
Optionally, the method that nonlinear regression diagnostic models can be used in the outlier detection, including looked on an independent variable X
To the conditional probability of another stochastic variable Y, exceptional value is distinguished using reverse search；Firstly, being constructed back using all data
Return model, then, sequentially or concurrently as a result, when hypothesized model is correct from excluding that there is worst error in model
When, true residue always has standardized normal distribution.
Optionally, neural network method can be used in the curve smoothing processing, and the form of the neural network method is more
Layer perceptron, and carries out Model Diagnosis, and residual error worm figure can be used in the Model Diagnosis, when all observed values all fall in two it is ellipse
The point in " receiving " region i.e. about 95% in circular curve falls between two elliptic curves and does not detect in observed value
When to specific shape, assert that the model overall fit is preferable.
Optionally, when past data sample amount is less than 30, the nonparametric quantizating index uses K-S statistic DKS.
Optionally, the outlier detection can also use box traction substation method, based on density-distance method or based on throwing
The method of shadow tracking.
The present invention provides a kind of comparison unit of SIMS analysis curve, whether there is for diagnosing ion implanting
It is abnormal, comprising:
Board fine-adjusting unit, for finely tuning board；
Decision package carries out the self checking of ion implantation dosage deviation for board, if ion implantation dosage deviation is less than
1%, then fine tuning board is re-started, if ion implantation dosage difference is more than or equal to 1%, is entered in next step；
Outlier detection unit, for carrying out outlier detection and rejecting；
Curve smoothing unit, for carrying out curve smoothing processing and carrying out Model Diagnosis；
Quantizating index computing unit, for calculating relevant nonparametric quantizating index；
Comparing unit carries out the ratio of SIMS analysis curve according to the calculated index of quantizating index computing unit
Compared with if the index meets threshold value, secondary ion injection is normal；If being unsatisfactory for threshold value, secondary ion injection is abnormal, then weighs
Newly it is finely adjusted board.
Optionally, the nonparametric quantizating index is " difference percentage D ", its calculation formula isWhereinGA(x) and GBIt (x) is two given SDP curve smoothings
Function, a represent shallow area's depth value, and b represents deep area depth value.
Optionally, the threshold definitions are 0.276%, i.e., as D≤0.276%, the sample to be tested and standard sample
SDP curve be it is analogous, this time inject normal, work as D > 0.276%, the sample to be tested and standard sample SDP curve exist
Significant difference, it this time injects abnormal.
Optionally, the nonparametric quantizating index be Ke Ermo can love-Si meter love K-S statistic DKS, formula is
DKS=max | F (x)-G (x) |, wherein F (x) and G (x) represents the empirical cumulative distribution function of two SDP curves.
Optionally, described device is not limited by sample distribution and population sample amount size；When the sample dimension is greater than 1
When, it can be in the maximum between the empirical cumulative distribution function described in All Quardrants for finding the sample under any possible sequence
Antipode.Optionally, when the dimension of the sample is 2, n sample point is provided in two-dimensional space, is calculated by all right
Empirical cumulative distribution function in the 4n2 quadrant for the plane that (Xi, Yj) is defined, and calculate the empirical distribution function in All Quardrants
Between maximum antipode, wherein Xi and Yj is the coordinate of any point pair in given sample, and counting step can pass through violence
Algorithm executes, and whether wherein which determines the point to the inswept each quadrant of each point in the sample.
Optionally, if significance a=0.05, the threshold definitions are 0.09, i.e., as DKS≤0.09, institute
State sample to be tested and standard sample SDP curve be it is analogous, this time ion implanting it is normal；Work as D > 0.09, the sample to be tested
It is that there are significant differences with standard sample SDP curve, this time injects abnormal.
Optionally, the method that nonlinear regression diagnostic models can be used in the outlier detection, including looked on an independent variable X
To the conditional probability of another stochastic variable Y, exceptional value is distinguished using reverse search；Firstly, being constructed back using all data
Return model, then, sequentially or concurrently as a result, when hypothesized model is correct from excluding that there is worst error in model
When, true residue always has standardized normal distribution.
Optionally, neural network method can be used in the curve smoothing processing, and the form of the neural network method is more
Layer perceptron, and carries out Model Diagnosis, and residual error worm figure can be used in the Model Diagnosis, when all observed values all fall in two it is ellipse
The point in " receiving " region i.e. about 95% in circular curve falls between two elliptic curves and does not detect in observed value
When to specific shape, assert that the model overall fit is preferable.
Optionally, when past data sample amount is less than 30, the nonparametric quantizating index uses K-S statistic DKS。
Optionally, the outlier detection can also use box traction substation method, based on density-distance method or based on throwing
The method of shadow tracking.
Detailed description of the invention
Fig. 1 is SIMS operation principle schematic diagram；
Fig. 2 is a kind of typical SDP curve graph (identification sample: 1 °, reference sample: 0 °) based on different implant angles；
Fig. 3 (a) is that identification sample matches good SDP curve graph with reference sample, and Fig. 3 (b) is identification sample and reference
The poor SDP curve graph of sample matches；
Fig. 4 is the division figure of area coordinate in K-method；
Drain current degradation figure when Fig. 5 is the saturation of two groups of samples in Fig. 3 (b)；
Fig. 6 is a kind of comparative approach flow chart of SIMS analysis curve provided by the invention；
Fig. 7 is to carry out abnormal point mapping based on case collimation method；
Fig. 8 is to carry out abnormal point mapping based on density-Furthest Neighbor；
Fig. 9 is to carry out abnormal point mapping based on Projection Pursuit method；
Figure 10 is the quartile figure of the residual error before and after suppressing exception value；
Figure 11 is to carry out abnormal point mapping based on regression diagnostics method；
Figure 12 is to compare figure using the SDP curve of different smoothing methods；
Figure 13 is the Visualization figure for carrying out neural network model；
Figure 14 is based on the smoothed out SDP curve graph of neural network；
Figure 15 is the residual plot of the SDP curve of reference sample in Fig. 3 (a)；
Figure 16 is the worm figure of the residual error of the SDP curve of reference sample in Fig. 3 (a)；
Figure 17 is the comparison figure of the SDP curve based on NRC method；
Specific embodiment
Below in conjunction with the drawings and specific embodiments to the comparative approach of SIMS analysis curve provided by the invention
And device is described in further detail.
Referring first to Fig. 6, a kind of comparative approach of SIMS analysis curve provided by the invention, comprising:
S1 finely tunes board；
S2, the first decision phase, board carries out the self checking of ion implantation dosage deviation, if ion implantation dosage deviation is less than
1%, then step S3 is gone to, if ion implantation dosage difference is more than or equal to 1%, goes to step S1；
S3 carries out outlier detection and rejects；
S4 carries out curve smoothing processing and carries out Model Diagnosis；
S5 calculates relevant nonparametric quantizating index and carries out the ratio of SIMS analysis curve according to the index
Compared with；
S6, if the index meets threshold value, secondary ion injection is normal；If being unsatisfactory for threshold value, secondary ion injection
It is abnormal, go to step S1.
Below with reference to Fig. 7-Figure 17, above-mentioned steps of the invention are described in detail.
A. outlier detection.
SDP provides ingredient composition and depth information.However, the identification of interface (shallow-layer) may be difficult.On the one hand,
Interface is usually very thin and usually marks the degree of approach of different materials, may have relatively different secondary ion yields.Separately
On the one hand, surface contamination may be a serious problem, because the particle on initial surface may also lead to secondary ion letter
In the sample that number secondary ion signal may be analyzed over head and ears and real Impurity Distribution is masked in statistics, these moulds
The imaginary signal for pasting true Impurity Distribution is considered as.Statistically, exceptional value is a kind of far from each other with other observation results
Observation is as a result, so that wake suspicion that it is generated by different mechanism.Exceptional value can seriously mislead prediction, and make global number
It is less accurate according to the deduction of collection.Therefore, identify and delete important and necessary that the exceptional value in real observation is statistical analysis
Business.
Most of classical ways for rejecting outliers are based on certain statistical distribution, and exceptional value is identified as having
Compared with those of lower probability of occurrence point.However, the distribution of SDP is unclear.By taking " Split " SDP in Fig. 3 b as an example.Four kinds of differences
Nonparametric technique be introduced for accurately identifying exceptional value.
1) Tukey method (box traction substation).
Although exceptional value relative rarity and uncommon, compared with other observe results, their importance is very high, makes
The detection for obtaining them is very crucial.In practical applications, only by utilizing some simple visual suitable figures, such as case
Line chart, it is easy to detect the exceptional value of single argument sample.Box traction substation is a kind of graphical display, for describing one by quartile
Group numeric data, the hypothesis without doing any basic statistical distribution.The width of box, be defined as interquartile-range IQR (IQR,
Interquartile range), be equal to third quartile (Q3,3rdQuartile first quartile (Q1,1) is subtractedst
quartile).IQR indicates the dispersion degree and the degree of bias in data, if lower than Q1-1.5 × IQR or being higher than Q3+1.5 × IQR,
Then a point is identified as exceptional value.
Similarly, for bivariate data, such as SDP, a kind of simple method is the reasonable interval of setting, then will
The types of variables of depth is converted to classified variable from continuous variable.Exceptional value in each category level is marked as case figure
Point outside beard.For in Fig. 3 b " Split " SDP, the types of variables of depth has been changed to classified variable, and depth
Corresponding interval be arranged to 10.As shown in fig. 7, depicting a series of box-shaped figures.It is obvious that almost all of exceptional value (by
It is a little bigger to indicate) shallow and deep depths is appeared at, correspond to interface ontology section.The physical interpretation that these discoveries are illustrated with front
Unanimously.
2) it is based on the method for density-distance (DD, density-distance).
Although being readily possible to detect exceptional value by box traction substation, the selection of interval has subjectivity.Therefore, it examines
Consider based on the method for density distance (DD) and avoids this subjective selection.This method needs to calculate, and there are the data of geometric interpretation to see
In addition the distance between measured value itself is exactly to detect and develop particular for multivariate outliers.This method also regardless of
Data distribution form, this is also one key advantages.
Classical way for detecting exceptional value is to calculate the distance between each data point and its neighbour, then those points
Density be assumed to be exceptional value significantly lower than its neighbour.Local outlier factor (LOF, local outlier factor) is base
In the concept of local density；The position is provided by k nearest-neighbors, and distance is close by the part of object for estimating that density passes through
Degree is compared with the local density of its neighbour, can identify that the region with similar density has with those than its neighbor density
The point of much lower density.These points are regarded as exceptional value.In order to determine the range of k nearest-neighbors, when calculating LOF
The k value used is set to 7.Box is labeled as by the exceptional value that LOF algorithm identifies in fig. 8.
3) method based on Projection Pursuit (PP, projection pursuit).
The computing cost of above LOF can not be ignored because it need to calculate data point and between all distances.In addition,
Although LOF to distribution do not make it is any it is assumed that it be not construed as pure nonparametric technique, because of its result pair
The selection of k is very sensitive, it is still desirable to specified (from experience=7).Projection Pursuit (PP, projection pursuit) is one
Kind is for searching the linear combination of variable so that the statistical technique of cluster can be presented to corresponding data for data.Its frame is set
It is set to optimization problem, target is to find projection index.The exceptional value that PP algorithm identifies marks in Fig. 9.
4) based on the method for regression diagnostics.
Regression analysis includes that the conditional probability of another stochastic variable Y is found on an independent variable X.Using reverse search
To distinguish exceptional value.Firstly, constructing regression model using all data.Then, tool is sequentially or concurrently excluded from model
There is the observation result of worst error.When hypothesized model is correct, true residue always has standardized normal distribution.Figure 10 is illustrated
(left side) and quartile (QQ) normal state figure of the residual error on (right side) later before suppressing exception value.
It is obvious that normal QQ figure is approximately linear (intercept 0 and gradient 1) after removing exceptional value；Exceptional value is being schemed
Label is in 11.
Although not only simple by using box traction substation detection exceptional value but also directly, the selection of interval be it is subjective and
It is uncertain.LOF is a kind of unsupervised value detection method that peels off, and it is close relative to the part of its neighbour that it calculates data-oriented point
Deviation is spent, without doing any hypothesis to distribution.But it is very sensitive to user-defined parameter k neighbours.PP is a kind of lookup change
The method for measuring linear combination, such data can provide cluster relevant to these variables；However, it can not simulate complexity
It generates model and height consumes computer time.Based on this, it is recommended to use nonlinear regression diagnostic models detect exceptional value.
B. curve smoothing: nonlinear regression.
Accurately estimate SDP potential function be reliable quantitative analysis most critical and most basic problem.Usual base
Parametric form is proposed in priori knowledge.However when these stringent parametric assumptions may cause partially in the case where inaccuracy
The estimation of difference.Since nonparametric smoothing method has very strong flexibility, several nonparametric techniques are compared, are obtained
The best features function of SDP.These nonparametric smoothing models are cubic spline interpolation (CSI, Cubic Spline
), Interpolation smooth (LOWESS, locally the weighted scatterplot of local weighted recurrence scatterplot
) and NNs smoothing；Their sharpening result is as shown in figure 12.
It is flexibly the approximating method of nonlinear regression model (NLRM) that NNs, which is provided a kind of, they are the non-thread of overparameterization
Property statistical model, this makes them very flexible, therefore can approximate any smooth function.They can look in explanatory variable
To high-order reciprocation, this is very difficult to traditional regression method.As shown in figure 12, the feature of SDP is (especially shallow
Place) it can only be portrayed completely by NN.Due to the overparameterization of NN, compared with more conventional smoothing method, they are difficult to explain.
The most common NN form is multilayer perceptron (MLP, multi-layer perceptron), is inputted by one,
One output and possible one or more hidden layer compositions.Input unit is inputted the list passed in first hidden layer
Member is directly passed to output unit.Each unit adding plus a constant (referred to as " deviation ") to its input in hidden layer
Quan He, and calculate activation primitive φhResult.The hidden unit or output unit being then passed in next layer.
Empirical studies show that multitiered network does not usually show more compared with the NN with one or two hidden layer
It is good and often worse.Therefore, method provided by the present invention is since the most simple but most common NN structure, containing only one
A hidden layer (to avoid the recurrence of overfitting single argument) and 10 nodes.Such as Figure 13, wherein thicker line indicates that coefficient has
The larger value.In Figure 13, I1 and O1 are to output and input item respectively；H1~H10 is concealed nodes.By activation primitive in hidden layer
In be set as tangent line hyperbolic functions and exponential function in output layer.Input is expressed as xi, for having a hidden layer
MLP exports tkIt can be obtained by formula (1):
tk=φ0(αk+∑j→kwjkφh(αj+∑i→jwijxi)) (1)。
Wherein, αkRepresent k non-linear neural member, wjkRepresent weight delay.
If only one output node, k is equal to 1.Power can be determined by optimizing some canonical functions appropriate
Weight for example minimizes the total of the square error of predictive variable and/or is maximized in the case where assume that the distribution of response variable
The log-likelihood of data.
The structure of MLP allow it to fitting output and input between very general nonlinear function.Research shows that
The NN for possessing enough hidden units can approach arbitrary function relationship.However, overfitting may be one under this framework
Serious problem.Usually by early stage stop optimization, or more ground punish optimisation criteria using Regularization Technique.By excellent
The estimation that addition penalty term carrys out optimisation criteria weight in change standard will be reduced, this is also referred to as contraction method.(2) is smooth in equation
Punishment is usually used in contraction method:
This process is also referred to as " weight decaying " in NN document；In Figure 13, two punishment nodes B1 and B2 are specified.
The use of weight decaying seems not only to facilitate optimization process but also avoids overfitting.Adjusting parameter k can by cross validation come
Selection minimizes formula (2) for the hidden unit of fixed quantity to obtain weight estimation.
Such as Figure 14, it is based on its diagnostic graph, the SDP in Fig. 2 and Fig. 3 has been carried out well smoothly, and as expected, NN can
Best to describe SDP behavior.The major advantage for normalizing quantile residual error is that vacation is worked as in the distribution regardless of response variable
If model is correct, true residue always has standardized normal distribution.Residual error performance is good.Because of the first two of residual error in Figure 15
It is the random scatter at 0 around horizontal linear line that the match value of depth and the match value of index and index, which are rendered as mean value, in figure；
And the Density Estimator of residual error is approximately normal distribution, QQ figure is approximately linear (intercept 0, gradient 1).In addition, its R2
Also very high, it is 0.994.
As shown in figure 16, to identify the region of explanatory variable, model cannot be abundant in the area for the worm figure of residual error
Fitting data (referred to as " model violation ").This is a diagnostic tool, for checking the difference of one or two explanatory variable
The residual error of range (not being overlapped under default situations).Since all observations all fall in " receiving " region in two elliptic curves (greatly
About 95% point is fallen between two elliptic curves) and do not detect on point specific shape, as shown in figure 16, the mould
Type seems the fine of overall fit.
The judgement that C.SDP compares.
The comparative approach of SDP can compare (NRC) by statistical method or by normalization ratio to quantify.
1) NRC method.
In order to preferably compare two by function GA(x) and GB(x) section provided, wherein x represents depth, can pass through
Diversity ratio can be write following expression by concentration normalization.
Obviously, formula (3), if Ratio (x)=1 is set up, the two sections can be identified as exactly matching.Therefore,
The problem of characterizing difference between the two profiles can be interpreted simply as how judging equation establishment.In order to obtain curve weight
The quantitative target of conjunction, using the integrated value of the per unit depth of the shadow region surrounded by horizontal line (Ratio (x)=1), referred to as
" difference percentage " can be calculated by formula (4):
Wherein, a represents lower limit of integral, and b represents upper limit of integral.
Method based on formula (4) is referred to as comparing (NRC) by statistical method or by normalizing ratio.
As shown in figure 17, (Fig. 3 a, 3b and each Ratio (x) function 2) are by different line type (respectively points by SDP
Line, dotted line and solid line) it draws.According to the technological requirements, lower and upper limit are respectively set as 20nm and 800nm.Meanwhile difference percentage
Ratio D mark is in tablei and the upper left corner of Figure 17 also has.Based on many experimental datas, by the threshold definitions of difference percentage
For 0.276% to judge whether two SDP are comparable.A possibility that from the point of view of common sense, difference percentage is smaller, two samples
It is bigger.Therefore, the SDP in Fig. 3 a is comparable, and other then different.
TABLE I
THE CALCULATED VALUES BASED ON NRC
2) Kolmogorov-Smirnov is examined
Kolmogorov-Smirnov (KS) inspection is distribution-free limitation, can be commonly used and not big by population sample amount
Small limitation.These are even more important for the comparison of two SDP, because their distribution is substantially unknown.
In general, KS inspection can be used for sample to be compared with reference to probability distribution, or compare two samples.Double sample KS
Examine it is more useful because it is sensitive to the difference of the location and shape parameter of the empirical cumulative distribution function (CDF) of two samples.
It has quantified the distance between experience distribution of two samples.The zero cloth of the statistic is calculated under null hypothesis, the vacation
If being sample is extracted from the same distribution in double sample situation.KS statistic, DKSIt is defined as DKS=max | F (x)-G
(x) |, F (x) and G (x) represents the CDF of two samples.
It is very challenging thing that KS statistic, which is expanded to hyperspace,.In one-dimensional sample, experience is distributed only
Change in given viewpoint, and obtains single argument by assessing the distance between experience and theoretic distribution function at these points
KS statistic.However, empirical distribution function can jump on unlimited number of point when dimension is greater than 1.Peacock describes logical
It crosses under any possible sequence and finds the maximum difference between CDF to make statistical iteration in the idea of any particular sorted.?
N point is provided in two-dimensional space, needs to calculate by all to (Xi,Yj) 4n of plane that defines2CDF in quadrant, wherein XiWith
YjIt is the coordinate of any point pair in given sample.Then, the maximum antipode in All Quardrants between CDF is calculated.Count step
Suddenly it can be executed by violence algorithm, whether which determines the point at it in inswept each quadrant of each point in sample
In.
Here, the comparison of two SDP is realized using the idea of Peacock, the counting statistics value of Fig. 2 and Fig. 3 are in Table II
In.If it is 0.090 that KS approximate calculation threshold value, which can be used, using α=0.05.Therefore, threshold value is lower than for KS statistical value, no
Refuse the null hypothesis that they are comparable.Such as the conclusion in Table II, the SDP in Fig. 3 a is comparable, and other (i.e. Fig. 2
And 3b) be not then.Conclusion is consistent (Figure 17 and Table I) with NRC.
TABLE II
THE CALCULATED KS STATISTIC VALUES
In short, NRC and KS test can handle well SDP and compare.In practice, their selection depends on practical
Situation.In particular, KS test can be more preferable when previous number is according to library not enough big (< 30).
The accuracy characteristic (energy, dosage and angle) of IMP can directly affect device performance, thus it is to semiconductors manufacture
For it is particularly significant.The present invention provides a kind of new methods with K-method before improving, this be a kind of pure nonparametric technique can
Quantizating index, without do any subjectivity it is assumed that can handle various shape, realize that SDP compares.Some exceptional values determine
Method is introduced into exclude exceptional value, is recommended to use nonlinear regression diagnostic models here.Neural network SDP the most flexible is non-linear
Recurrence is used to smooth SDP curve.In fact, four kinds of different exceptional value identification methods right and wrong for industry practitioner
The reference of Chang Youyong is beneficial to nearly all analysis of statistical data.Finally, by means of both non-parametric methods of KS and NRC
Quantifiable index can be obtained to compare for SDP.When the record that database includes in the early time is less than 30, KS method may
It is a better choice.These readily understood certifiable methods facilitate early monitoring and practitioner are instructed to complete corresponding solution
Certainly method reduces the influence of deviation.
Obviously, those skilled in the art can carry out various changes without departing from spirit and model of the invention to the present invention
It encloses.In this way, if these modifications and changes of the present invention is within the scope of the claims of the present invention and its equivalent technology, then
This law is bright to be also intended to including these modification and variations.
Claims (10)
1. a kind of comparative approach of SIMS analysis curve, for diagnosing ion implanting with the presence or absence of abnormal, feature
It is, comprising the following steps:
S1 finely tunes board；
S2, the first decision phase, board carry out the self checking of ion implantation dosage deviation, if ion implantation dosage deviation less than 1%,
Step S3 is then gone to, if ion implantation dosage difference is more than or equal to 1%, goes to step S1；
S3 carries out outlier detection and rejects；
S4 carries out curve smoothing processing and carries out Model Diagnosis；
S5 calculates relevant nonparametric quantizating index and carries out the comparison of SIMS analysis curve according to the index；
S6, if the index meets threshold value, secondary ion injection is normal；If being unsatisfactory for threshold value, secondary ion injection is abnormal,
Go to step S1.
2. the comparative approach of SIMS analysis curve as described in claim 1, which is characterized in that the nonparametric amount
Changing index is " difference percentage D ", its calculation formula isWhereinGA
(x) and GBIt (x) is two given SDP curve smoothing functions, a represents shallow area's depth value, and b represents deep area depth value.
3. the comparative approach of SIMS analysis curve as claimed in claim 2, which is characterized in that the threshold definitions
It is 0.276%, i.e., as D≤0.276%, the sample to be tested and standard sample SDP curve are analogous, this time injections
Normally.Working as D > 0.276%, the sample to be tested and standard sample SDP curve, there are significant differences, this time inject abnormal.
4. the comparative approach of SIMS analysis curve as described in claim 1, which is characterized in that the nonparametric amount
Changing index is that Ke Ermo can love-Si meter love K-S statistic DKS, formula DKS=max | F (x)-G (x) |, wherein F
(x) empirical cumulative distribution function of two SDP curves is represented with G (x).
5. the comparative approach of SIMS analysis curve as claimed in claim 4, which is characterized in that the method not by
The limitation of sample distribution and population sample amount size；When the sample dimension is greater than 1, can be found under any possible sequence
Maximum antipode between the empirical cumulative distribution function described in All Quardrants of the sample.
6. the comparative approach of SIMS analysis curve as claimed in claim 5, which is characterized in that when the sample
When dimension is 2, n sample point is provided in two-dimensional space, calculates the 4n by all planes defined to (Xi, Yj)2In quadrant
Empirical cumulative distribution function, and calculate the maximum antipode between the empirical distribution function in All Quardrants, wherein Xi and
Yj is the coordinate of any point pair in given sample, and counting step can be executed by violence algorithm, and the algorithm is in the sample
The inswept each quadrant of each point, whether wherein determine the point.
7. the comparative approach of the SIMS analysis curve as described in any one of claim 4-6, which is characterized in that such as
Fruit significance a=0.05, then the threshold definitions are 0.09, that is, work as DKSWhen≤0.09, the sample to be tested and standard sample
Product SDP curve be it is analogous, this time ion implanting it is normal.Work as D > 0.09, the sample to be tested and standard sample SDP curve are
There are significant differences, this time inject abnormal.
8. the comparative approach of SIMS analysis curve as described in claim 1, which is characterized in that the abnormal point
The method that nonlinear regression diagnostic models can be used is surveyed, the condition including finding another stochastic variable Y on an independent variable X is general
Rate distinguishes exceptional value using reverse search；Firstly, constructing regression model using all data, then, sequentially or concurrently
As a result, when hypothesized model is correct from excluding to have worst error in model, true residue always has standard normal
Distribution.
9. the comparative approach of SIMS analysis curve as described in claim 1, which is characterized in that the curve smoothing
Neural network method can be used in processing, and the form of the neural network method is multilayer perceptron, and carries out Model Diagnosis, described
Residual error worm figure can be used in Model Diagnosis, when all observed values all fall in " receiving " region in two elliptic curves i.e. about
95% point is fallen between two elliptic curves and when not detecting specific shape in observed value, assert that the model is whole
Body fitting is preferable.
10. the comparative approach of SIMS analysis curve as claimed in claim 4, which is characterized in that work as past data
When sample size is less than 30, the nonparametric quantizating index uses K-S statistic DKS。
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| CN111191633A (en) * | 2020-01-14 | 2020-05-22 | 中国人民解放军国防科技大学 | Method, system and medium for exploring target curve from known data sequence |
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| CN110532681A (en) * | 2019-08-28 | 2019-12-03 | 哈尔滨工业大学 | Combustion engine method for detecting abnormality based on NARX network-box traction substation and normal schema extraction |
| CN111191633A (en) * | 2020-01-14 | 2020-05-22 | 中国人民解放军国防科技大学 | Method, system and medium for exploring target curve from known data sequence |
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