Cartographic Modeling of Electrostatic Charges for

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Transcript Cartographic Modeling of Electrostatic Charges for

Cartographic Modeling of Electrostatic
Charges for Semiconductor
Manufacturing
Mark Hogsett
Novx Corporation
[email protected]
I. Introduction
• The trend in metrology and analysis for
semiconductor manufacturing has been accelerating
as technology nodes (ITRS) continually migrate
toward higher density.
• Manufacturing processes are being subjected to
increased monitoring as yield and process
relationships become increasingly more complex.
• This would appear to argue that electrostatic
variables need to be measured in complementary
fashion.
2
Introduction
• As much subjectivity as possible
needs to be removed from the process
of investigation.
• The tools exist to measure the full
range of electrostatic variables, but
are often not applied in a rigorous
fashion.
3
II. Cartographic Method
• Since the central question in most electrostatic
investigations is potential charge distribution, the
question becomes one of location.
• In investigating a process, we are typically involved
in “mapping” areas of charge or voltage, the
presence and origin of electrostatic fields and the
spatial relationship between elements.
• Product and process materials can have fixed or
mobile charges.
• Charges of different polarity can exist on product
simultaneously.
4
Cartographic Method
• Charge levels can change as product moves through the
manufacturing process.
• This presents varying levels of risk to process and
product, involving tool reliability and product yield.
• It is possible to conduct systematic mapping of product,
tool surfaces and the product pathways throughout the
fab.
• If data collection is done carefully, an “electrostatic map”
can be produced and monitored.
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II. Data Collection
• Measuring charge, voltage or electrostatic fields for
wafers, reticles, carriers, work surfaces, storage, etc.
• Interactive (human) production data collection methods
are necessary where automated sensing is not feasible.
• Real time audio data recording allows high-volume
collection and description of measurements for
comprehensive data sets.
• Through adaptive sampling, data can be collected
through systematic and random sampling methods to
address specific issues and goals.
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Data Collection
• Measurement methods and tools need to be evaluated on
the basis of what type of data they can provide.
• Example: where charge/field polarity issues are
important, Faraday cup measurements may have to be
augmented or supplanted with other tools capable of
greater discrimination.
• Physical measurement constraints may require alternative
methods.
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Measurement Tools
Electrostatic Voltmeters
Nanocoulomb meters
Electrometers
8
Measurement Tools
Oscilloscopes
ESD Detectors
Faraday Cups
Electrostatic Field meters
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Measurement Points (wafer example)
Different sampling methods can be used (systematic vs. random)
10
Event Histograms (ESD)
11
Characterization Sampling Methods
• For general characterization studies, random sample sets
can vary in number and location.
• Typically, a minimum sample size per object is specified in
advance, with over-sampling not a problem.
• Sample measurement spacing can be based upon
equidistance criteria (i.e., predetermined sample density).
• Sparse sampling can often be addressed through reduced
sample probability methods.
12
Discrete Point Sampling Methods
• Systematic sampling methods can be used to measure
specific locations/features.
• Where specific location measurements are required,
sequential measurement points are determined from a
constant reference location.
• Examples: FOUP touch points
Reticle Pod handles
Wafer edges
End-effector contact points
13
III. Data Analysis
• A wealth of process information is available when data is
collected and analyzed systematically and statistically.
• System behaviors (states) can be analyzed in clear
temporal and spatial dimensions.
• This allows for better individual variable characterization.
• Data can be used to construct follow-on hypothetical
models (hypothesis testing) .
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Data Analysis…
• Allows robust inferences about real world conditions.
• Provides quality data of use to other
researchers/investigators (“blind data” with/without
attribution).
• Allows for longitudinal studies to be conducted for larger
issues.
• Allows for data comparability across studies.
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Data Analysis…
• Provides meaningful data to engineering applications and
general facility contamination models.
• Individual process element models can be used to
construct sophisticated risk models for larger processes.
• Models can indicate where a process can benefit from
dedicated sensing methods.
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Analysis: Measurements with Confidence
Sets
Electrostatic voltage sampling measurements, taking into account
measurement error (standard).
Points Volts
X[1]
X[2]
X[3]
X[4]
X[5]
X[6]
X[7]
X[8]
X[9]
X[10]
Sigma
950.0
5.789
30.0
5.736 17.38
22.0
5.691 9.675
102.0
5.68 89.56
62.0
5.839 49.39
140.
5.803 127.6
-74.0
5.692
-24.0
5.735
-43.0
5.813
-801.0
5.782
2.5%
97.5%
937.4
42.24
34.56
114.4
74.88
153.1
-86.53
-36.48
-55.5
-813.6
962.7
-61.79
-11.64
-30.23
-788.2
Example of wafer surface (topside) measurements.
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Analysis: Individual Point Measurement
Probabilities
Individual test points can be evaluated for contributions to the
vector field
potential and real contamination collection vectors as multinomial
distributions.
+V Points
X[1]
X[2]
X[3]
X[4]
X[5]
X[6]
-V Points
Sn[1]
Sn[2]
Sn[3]
Sn[4]
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P(X)
0.7275
0.0229
0.0168
0.07811
0.04749
0.1071
sd
0.0123
0.004157
0.00354
0.007419
0.005876
0.00855
2.5%
0.703
0.01549
0.01058
0.06409
0.03665
0.09116
97.5%
0.7511
0.03174
0.02426
0.09317
0.0598
0.1246
0.07861
0.02544
0.0456
0.8503
0.008738
0.005165
0.006798
0.01161
0.06226
0.01633
0.03328
0.8266
0.09634
0.03636
0.05967
0.8724
Analysis: Wafer Charge Example
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•
If you measure a wafer with bivalent charges at near
surface, you get a map of charge distribution by location.
•
If you measure the same surface at a height of 15cm, you
get the vector sum potential for all of the charges.
ESD Event Distribution Frequency by
Amplitude
WP7300 histogram from sequence capture mode.
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Derived Probability Densities
Same event distribution viewed as a Gaussian* probability density.
*Note tail
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Multinomial Distributions by Frequency
Data with non-Gaussian distributions can indicate
multiple phenomena, states or sources.
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Non-Gaussian Distributions
Beware of inappropriate averaging (means).
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Multinomial
Distributions for
ESD Events
Event
Prob
Std Dev
X[1]
0.007
0.023
X[2]
0.007
0.024
X[3]
0.011
0.031
X[4]
0.005
0.020
X[5]
0.020
0.040
X[6]
0.017
0.037
ESD event distributions for
X[7]
0.014
0.033
comparative peak amplitude can
X[8]
0.019
0.041
also be characterized using
X[9]
0.015
0.034
X[10]
0.021
0.042
multinomial probability distributions
X[11]
0.002
0.012
(in this case a Dirichlet distribution,
X[12]
0.015
0.035
which gives the probability for
X[13]
0.021
0.042
X[14]
0.021
0.040
X[15]
0.001
0.009
X[16]
0.006
0.021
X[17]
0.002
0.014
X[18]
0.012
0.030
X[19]
0.137
0.099
X[20]
0.143
0.101
X[21]
0.112
0.090
X[22]
0.116
0.092
X[23]
0.143
0.099
X[24]
0.134
0.098
individual measures for discrete
distributions).
This can be of use in interference
modeling and investigations.
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ESD Events by Frequency of Occurrence
A Poisson distribution gives the probability of occurrence at
any time t for a stochastic event series. It is typically used to
calculate rate probabilities across time periods.
Time Period
(minutes)
120
120
120
120
120
ESD Events
(counts)
12
29
21
58
91
Test Period
Period[1]
Period[2]
Period[3]
Period[4]
Period[5]
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As %
11
24
18
48
75
Prob
0.1059
0.2445
0.1791
0.4832
0.7554
sd
0.02983
0.04464
0.03884
0.06324
0.07816
2.5%
0.0555
0.1656
0.1118
0.3674
0.6107
97.5%
0.1716
0.3394
0.264
0.6147
0.9154
Composite Models
Example: Poisson distributions for ESD event frequency for two (2)
different tools across five (5) different test periods.
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Some Analytical Methods
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•
GLM (General Linear Regression Models)
•
Multivariate Analysis
•
MCMC (Markov Chain Monte Carlo)
•
ANOVA
•
Bayesian Network Analysis (BNAs)
•
Log Odds Ratios for model comparison
Conclusion
• Sound data collection methods coupled with analysis can
yield useful results.
• The choice of analytical tools and methods ranges from
basic to complex.
• In an increasingly data driven manufacturing
environment, scrutiny for electrostatic evaluation
methods will arguably intensify.
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References
‘Process Investments Control Support
Technology, Cut Costs’
Becky Pinto, KLA-Tencor, San Jose,
Semiconductor International 12/1/2005
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