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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.
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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.
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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.
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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
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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.
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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
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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
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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.
28
References
‘Process Investments Control Support
Technology, Cut Costs’
Becky Pinto, KLA-Tencor, San Jose,
Semiconductor International 12/1/2005
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