CN100587636C - Method for estimation and monitoring of plasma etching technology - Google Patents
Method for estimation and monitoring of plasma etching technology Download PDFInfo
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- CN100587636C CN100587636C CN200710062847A CN200710062847A CN100587636C CN 100587636 C CN100587636 C CN 100587636C CN 200710062847 A CN200710062847 A CN 200710062847A CN 200710062847 A CN200710062847 A CN 200710062847A CN 100587636 C CN100587636 C CN 100587636C
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Abstract
The invention relates to a prediction and detection method of plasma etching technique, which comprises adding object data sample into a preset pivot regression equation to obtain present processing performance indexes of plasma etching technique, and deciding to end the plasma etching technique or not according to the processing performance indexes of present plasma etching process. The inventioncan online detect the etching speed and uniformity of processed wafer.
Description
Technical field
The present invention relates to the detection and the monitoring technique field of equipment, relate in particular to a kind of prediction and method for supervising of plasma etching industrial.
Background technology
Along with the fast development of microelectronics and integrated circuit industry, the size of the semiconductor crystal wafer Wafer of plasma etching industrial process processing becomes increasing, and on the other hand, the critical size of grid etch is then reducing gradually.In order to guarantee second conductor wafer of this high novel technique etching quality of silicon chip just, need in art production process, monitor, technology trouble is diagnosed and predicting the emphasis parameter product quality.
The most frequently used a kind of process control technology is exactly pivot analysis (PCA) and Hotelling T at present
2Statistical method, its ultimate principle are according to the historical data under the existing normal process, according to the standard of setting, adopt the method for adding up to find out and can represent the low-dimensional pivot composition between each variable, i.e. principal component model under the normal process; For a sample to be detected, adopt principal component model to calculate its corresponding Hotelling T earlier
2Statistic, and, just can realize the fault diagnosis of technology in conjunction with the control limit that precomputes; When finding that technology has fault to take place, according to the scatter diagram of pivot and the score contribution plot of pivot, just can find out the reason that causes that technology breaks down again.
But, in technological process, having only quality testing, these control technologys of fault diagnosis is to meet the demands, in the process that technology is carried out, process engineers also wish to observe in real time some important process performance index (as etch rate, the etching homogeneity of technology), determine whether to finish present technological process.And these process performance index are immeasurable in the process that technology is carried out, and can only wait silicon chip to carve afterwards just energy measurement.
The existing main method that is used to obtain silicon chip erosion speed and etching homogeneity is the manual measurement method, as Fig. 1 and shown in Figure 2, it specifically is earlier to measure the thickness of diverse location before and after etching on the silicon chip with film thickness measuring instrument, again with the front and back film thickness difference (thickness that etches away) of all location points etching time divided by technology, just can obtain the etch rate of each position on the silicon chip, at last all etch rates are averaged, just can obtain the average etch rate of this sheet Wafer; And for the etching homogeneity of Wafer, then be the standard deviation of calculating the etch rate of each position on the silicon chip earlier, again with this standard deviation divided by the average etch rate of Wafer, resulting ratio is the etching homogeneity of this sheet Wafer.
This manual measurement method is to obtain the main method of etch rate and the etching homogeneity of Wafer present stage, its fundamental purpose is to check the etching performance of plasma etching machine by etch rate that measures and homogeneity, the stability of state and etching, this method can also be used in the process of making etching apparatus, but using etching apparatus to carry out in the technological process, this kind method can't be used, as seen this method can not realize technology carry out in etch rate and the inhomogeneity on-line monitoring of Wafer, thereby can not realize the on-line optimization of product performance index and the FEEDBACK CONTROL of explained hereafter.
Summary of the invention
At the technological deficiency that exists in the prior art scheme, the purpose of this invention is to provide a kind of prediction and method for supervising of plasma etching industrial, can realize technology carry out in etch rate and the inhomogeneity on-line monitoring of Wafer.
The objective of the invention is to be achieved through the following technical solutions:
A kind of prediction of plasma etching industrial and method for supervising comprise:
A, the pivot regression equation that data sample substitution to be detected is set draw the current process performance index of plasma etching industrial process;
B, according to the process of the process performance index predict process process of current plasma etching industrial process, determine whether to finish the plasma etching industrial process.
Described steps A comprises:
A1, data sample substitution principal component model equation to be detected is drawn each pivot value, and the pivot regression equation that each pivot value substitution is set is drawn the current process performance index of plasma etching industrial process; Perhaps,
A2, the pivot regression equation that the substitution of principal component model equation is set obtain target pivot regression equation, and data sample substitution target pivot regression equation to be detected are drawn the current process performance index of plasma etching industrial process.
The pivot regression equation of described setting is:
Y＝a
1×f
1+a
2×f
2+…+a
e×f
e；
In the formula,
Y, the output variable of equation, the output process performance index comprises etch rate or homogeneity;
a
1, a
2,+... +, a
e, the regression coefficient of equation;
f
1, f
2..., f
e, the pivot value in the principal component model equation;
E, the pivot number of equation.
Regression coefficient a in the described pivot regression equation
1, a
2,+... +, a
eWith pivot value f
1, f
2..., f
eHistorical data sample according to the plasma etching industrial process is determined.
Regression coefficient a in the described pivot regression equation
1, a
2,+... +, a
e, can determine by the method for multiple linear regression.
The principal component model equation is in the described pivot regression equation,
In the formula,
f
1, f
2..., f
e, the pivot value of equation;
x＝[x
1，x
2，…，x
m]
T。Wherein, x
1, x
2..., x
mIt is the process variable of technology;
p
1, p
2..., p
mInitial sample data correlation matrix X
N * mProper vector p
1, p
2..., p
mAnd, X
N * mFor choose the initial sample data correlation matrix that initial sample data is set up from the historical data sample of plasma etching industrial process.
Definite principle of the pivot number in the described pivot regression equation is that the information that new pivot variable is covered must reach more than 85% of former variable.
As seen from the above technical solution provided by the invention, the prediction of a kind of plasma etching industrial of the present invention and method for supervising, the pivot regression equation that data sample substitution to be detected is set draws the current process performance index of plasma etching industrial process; Process performance index according to current plasma etching industrial process determines whether to finish kind of a plasma etching industrial process again.Can realize technology carry out in etch rate and the inhomogeneity on-line monitoring of Wafer.
Description of drawings
Fig. 1 is a semiconductor wafer surface distribution schematic diagram one;
Fig. 2 is a semiconductor wafer surface distribution schematic diagram two;
Fig. 3 is technology etch rate PCR prediction effect figure;
Fig. 4 is the prediction effect figure of technology etching homogeneity.
Embodiment
For prior art problems, the common mathematical method is come some important parameters in the predict process production.This patent adopts the method for pivot analysis (PCA) and multiple linear regression (MVR) to provide a kind of Forecasting Methodology that is used for etching technics etch rate and etching homogeneity.Experimental result shows that the precision of prediction of this method satisfies the existing processes standard basically, and it is for the quality that improves technology and realize that the FEEDBACK CONTROL of technology can play important effect.
The prediction of a kind of plasma etching industrial of the present invention and method for supervising, its embodiment is:
The pivot regression equation of data sample substitution setting to be detected is drawn the current process performance index of plasma etching industrial process; According to the process of the process performance index predict process process of current plasma etching industrial process, determine whether to finish kind of a plasma etching industrial process again.
Dual mode is specifically arranged,
One, data sample substitution principal component model equation to be detected is drawn each pivot value, and the pivot regression equation that each pivot value substitution is set is drawn the current process performance index of plasma etching industrial process; Process performance index according to current plasma etching industrial process determines whether to finish kind of a plasma etching industrial process again.
Two, the pivot regression equation that the substitution of principal component model equation is set obtains target pivot regression equation, and data sample to be detected (should be the data sample of standard normalization) substitution target pivot regression equation is drawn the current process performance index of plasma etching industrial process.Process performance index according to current plasma etching industrial process determines whether to finish kind of a plasma etching industrial process again.
The pivot regression equation of above-mentioned setting is:
Y＝a
1×f
1+a
2×f
2+…+a
e×f
e；
In the formula,
Y, the output variable of equation, the output process performance index comprises etch rate or homogeneity;
a
1, a
2,+... +, a
e, the regression coefficient of equation;
f
1, f
2..., f
e, the pivot value in the principal component model equation;
E, the pivot number of equation.
Regression coefficient a in the pivot regression equation here
eWith pivot value f
eHistorical data sample according to the plasma etching industrial process is determined.
The principal component model equation is in the above-mentioned pivot regression equation,
In the formula,
f
1, f
2..., f
e, the pivot value of the technology of equation;
x＝[x
1，x
2，…，x
m]
T。Wherein, x
1, x
2..., x
mIt is the process variable of technology; , it is generally by chamber pressure (Pressure), process gas (gas) and chamber temp (Temperature), top electrode and adaptation (parameter such as RF andMatch is formed).
p
1, p
2..., p
mInitial sample data correlation matrix X
N * mEigenvalue
1〉=λ
2〉=... 〉=λ
mCorresponding proper vector p
1, p
2..., p
mAnd, X
N * mFor choose the initial sample data correlation matrix that initial sample data is set up from the historical data sample of plasma etching industrial process.
Its detailed process is as follows,
Step 1: from initial sample data of choosing of historical data sample and pre-service, this part work also is the most important condition of setting up principal component model and pivot regression equation.The rationality that initial sample data is chosen has directly determined the accuracy and the validity of the pivot set up, in order to guarantee this point, must note following problem when choosing data:
(1) rationality of data sample size;
(2) consistance of data sample type;
(3) standard normalization of data sample.
Based on above-mentioned standard, the data sample that present embodiment is chosen in the table 1 is example (because data sample is excessive, just not providing its concrete numerical value in the present patent application in detail):
Table 1
| Wafer ID | Data type | Etch rate | Etching homogeneity |
| HZ000897-19 | ME(60s) | 1840.09 | 2.93％ |
| HZ000897-20 | ME(60s) | 1814.90 | 2.51％ |
| HZ000897-21 | ME(60s) | 1827.83 | 2.63％ |
| HZ000897-22 | ME(60s) | 1902.76 | 2.78％ |
| HZ000897-23 | ME(60s) | 1865.18 | 2.71％ |
| HZ000897-24 | ME(60s) | 1813.81 | 2.58％ |
| HZ000897-25 | ME(60s) | 1840.16 | 2.50％ |
| HZ000898-11 | ME(60s) | 1836.79 | 2.51％ |
| HZ000898-12 | ME(60s) | 1874.47 | 2.60％ |
| HZ000898-13 | ME(60s) | 1801.95 | 2.45％ |
| HZ000898-14 | ME(60s) | 1919.32 | 2.68％ |
| HZ000898-15 | ME(60s) | 1759.81 | 2.37％ |
| HZ000898-16 | ME(60s) | 1824.39 | 2.30％ |
| HZ000898-17 | ME(60s) | 1849.79 | 2.55％ |
| HZ000898-18 | ME(60s) | 1854.40 | 2.39％ |
| HZ000898-19 | ME(60s) | 1829.28 | 2.46％ |
| HZ000898-20 | ME(60s) | 1853.08 | 2.67％ |
| HZ000898-21 | ME(60s) | 1828.56 | 2.17％ |
Can set up initial sample data correlation matrix X thus
N * mWherein n is a sample number, and m is the variable number of process performance index;
Step 2: the foundation of principal component model, this step mainly comprises following process:
(1) initial this correlation matrix of sample data X
N * mThe calculating of (, then only needing to calculate its covariance matrix) if initial sample has passed through standard normalization;
(2) compute matrix X
N * mEigenvalue
1〉=λ
2〉=... 〉=λ
mWith corresponding proper vector p
1, p
2..., p
m
(3) determine needed pivot number in the principal component model (definite principle of pivot number is that the information that new pivot variable is covered must reach more than 85% of former variable).
For example, if being 6, the pivot number of determining (might as well use f
1, f
2..., f
6Expression), the technology principal component model of then being set up is:
In the formula, x=[x
1, x
2..., x
m]
TBe initializaing variable.
Step 3: the foundation of pivot regression equation.According to above-mentioned technology principal component model, calculate the score vector of all initial samples, and with its form one sub matrix, be somebody's turn to do to such an extent that sub matrix that is to say input variable in the pivot regression equation, on the other hand, as output variable (also must carry out standard normalization), adopt the method for multiple linear regression to set up the equation of linear regression of input variable and output variable at last the variable (etch rate and homogeneity) that needs in the etching technics to predict.If establishing Y is output variable, f
1, f
2..., f
6Be 6 pivots having determined, then the form of pivot regression equation is:
Y=a
1* f
1+ a
2* f
2+ ... + a
6* f
6(equation 2)
A wherein
1, a
2,+... +, a
6Regression coefficient.Regression coefficient can be determined by the method for multiple linear regression.Concrete steps are: with the variable (etch rate and homogeneity) that needs in the etching technics to predict as output variable, with initial sample sub matrix as input variable, adopt the method for multiple linear regression can determine each regression coefficient at last.
Based on historical data given in the preamble, the method that this patent adopts pivot analysis and pivot to return has obtained the regression equation of etch rate under the corresponding process conditions and etching homogeneity, its concrete condition is as follows, represents the etch rate function, represents the etching homogeneity function with U with V:
V＝-0.0069f
1+0.0082f
2-0.4367f
3-0.2704f
4+0.1431f
5+0.4184f
6
U＝0.1466f
1-0.1359f
2-0.1504f
3-0.1620f
4-0.2585f
5+0.4632f
6
For a sample to be detected, at first with its standard normalization, the pivot that adopts principal component model (equation 1) to calculate each pivot again gets score value, with above-mentioned two regression equations of resulting value substitution, just can dope pairing etch rate of this technology sample and homogeneity at last.Etch rate and homogeneity according to current plasma etching industrial process determines whether to finish kind of a plasma etching industrial process again.
In addition, be the mature technology scheme, the present invention also comprises:
Step 4: the check of pivot regression equation.In order to investigate the degree of accuracy of above-mentioned forecast model, also must adopt certain experimental data that above-mentioned model is tested, and constantly above-mentioned model is adjusted (pivot is a regression coefficient) according to each assay, thereby make the relative error of prediction meet technological standards.
Based on above step, as shown in table 1, adopted the historical data of 18 groups of etching technics that above-mentioned forecast model is checked in this patent, the result who obtains is as shown in table 2, be not difficult to find from result calculated: the method that given pivot returns this patent is that comparison is effectively with accurately for the parameter prediction of etching technics, the relative error (ratio of the standard deviation of predicted value, actual value and the mean value of actual value) of picture etch rate has only 0.75%, and the relative error of etching homogeneity also has only 2.66%.Certainly, cause the main cause that has error between predicted value and the actual value that 2 points are arranged: the one, cause the variation coefficient in principal component model and the regression model to have error because initial sample data is very few, on the other hand then because actual value itself also exists the certain measuring errors and the error of calculation (actual value is by calculating behind the manual measurement again).
Table 2
The technology that returns by pivot analysis and pivot among the present invention has provided a kind of etching technics etch rate and inhomogeneity real-time predicting method of being used for, result of calculation shows: this method is very effective, the relative error of its prediction meets existing technological standards fully, if this technology is promoted perfect and sequencing (being integrated in the technology controlling and process software), can better realize robotization control and FEEDBACK CONTROL in the etching technics, thereby avoid manual measurement and calculate etch rate, inhomogeneity complicacy improves existing work efficiency to a certain extent.As shown in Figure 3, shown in Figure 4 for technology etch rate PCR prediction effect figure, be the prediction effect figure of technology etching homogeneity.
The method that returns by pivot analysis and pivot among the present invention has provided etch rate and the etching homogeneity equation of linear regression (equation 2) about pivot, like this for a sample z=[z to be detected
1, z
2..., z
m]
T, at first only need to calculate the get score value of sample z to each pivot by principal component model (equation 1), with resulting value substitution pivot regression equation, just can dope pairing etch rate of sample z and homogeneity again.And in fact, if principal component model (equation 1) is updated in the pivot regression equation (equation 2), just can obtain the equation of linear regression of etch rate (homogeneity) about former variable, and in this case, only need known detection sample (process standard normalization earlier) is updated in this regression equation, also can obtain the etch rate (homogeneity) of respective sample.
Be the preferable embodiment of the present invention; but protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses, the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.
Claims (4)
1, a kind of prediction of plasma etching industrial and method for supervising is characterized in that, comprise step:
A, the pivot regression equation that data sample substitution to be detected is set draw the current process performance index of plasma etching industrial process;
B, according to the process of the process performance index predict process process of current plasma etching industrial process, determine whether to finish the plasma etching industrial process;
Described steps A comprises:
A1, data sample substitution principal component model equation to be detected is drawn each pivot value, and the pivot regression equation that each pivot value substitution is set is drawn the current process performance index of plasma etching industrial process; Perhaps,
A2, the pivot regression equation that the substitution of principal component model equation is set obtain target pivot regression equation, and data sample substitution target pivot regression equation to be detected are drawn the current process performance index of plasma etching industrial process;
The pivot regression equation of described setting is:
Y＝a
1×f
1+a
2×f
2+…+a
e×f
e；
In the formula,
Y, the output variable of equation, the output process performance index comprises etch rate or homogeneity;
a
1, a
2..., a
e, the regression coefficient of equation;
f
1, f
2..., f
e, the pivot value in the principal component model equation;
E, the pivot number of equation;
The principal component model equation is in the described pivot regression equation:
In the formula,
f
1, f
2..., f
e, the pivot value of equation;
X=[x
1, x
2..., x
m]
TWherein, x
1, x
2..., x
mIt is the process variable of technology;
p
1, p
2..., p
mInitial sample data correlation matrix X
N * mProper vector p
1, p
2..., p
mAnd, X
N * mFor choose the initial sample data correlation matrix that initial sample data is set up from the historical data sample of plasma etching industrial process; Wherein n is a sample number, and m is the variable number of process performance index.
2, the prediction of plasma etching industrial according to claim 1 and method for supervising is characterized in that, the regression coefficient a in the described pivot regression equation
1, a
2..., a
eWith pivot value f
1, f
2..., f
eHistorical data sample according to the plasma etching industrial process is determined.
3, the prediction of plasma etching industrial according to claim 2 and method for supervising is characterized in that, the regression coefficient a in the described pivot regression equation
1, a
2..., a
e, can determine by the method for multiple linear regression.
4, the prediction of plasma etching industrial according to claim 1 and method for supervising is characterized in that, definite principle of the pivot number in the described pivot regression equation is that the information that new pivot variable is covered reaches more than 85% of former variable.
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|---|---|---|---|
| CN200710062847A CN100587636C (en) | 2007-01-18 | 2007-01-18 | Method for estimation and monitoring of plasma etching technology |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN200710062847A CN100587636C (en) | 2007-01-18 | 2007-01-18 | Method for estimation and monitoring of plasma etching technology |
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|---|---|
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| CN100587636C true CN100587636C (en) | 2010-02-03 |
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Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102117731B (en) * | 2009-12-31 | 2013-01-02 | 中芯国际集成电路制造(上海)有限公司 | Method and device for monitoring measurement data in process production flow of semiconductor |
| CN106298573A (en) * | 2016-09-13 | 2017-01-04 | 冠礼控制科技（上海）有限公司 | The method of testing of rate of etch is improved by silicon chip spinning and oscillating mechanism |
| CN106840820B (en) * | 2016-11-29 | 2020-10-23 | 信利（惠州）智能显示有限公司 | CVD film and etching treatment method thereof |
| CN109919923B (en) * | 2019-02-28 | 2023-06-02 | 上海集成电路研发中心有限公司 | Analysis system and method for etching pattern |
| CN110850812B (en) * | 2019-11-18 | 2020-07-31 | 北京邮电大学 | Ion beam etching rate control method and device based on model |
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Address after: 100176 Beijing economic and Technological Development Zone, Wenchang Road, No. 8, No. Patentee after: Beijing North China microelectronics equipment Co Ltd Address before: 100016, building 2, block M5, No. 1 East Jiuxianqiao Road, Beijing, Chaoyang District Patentee before: Beifang Microelectronic Base Equipment Proces Research Center Co., Ltd., Beijing |
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