Cartographic Modeling of Electrostatic Charges for Semiconductor

Manufacturing

Mark Hogsett

Novx Corporation

mark@novxcorp.com

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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)

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Event Histograms (ESD)

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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

Points Volts Sigma 2.5% 97.5%X[1] 950.0 5.789 937.4 962.7X[2] 30.0 5.736 17.38 42.24X[3] 22.0 5.691 9.675 34.56X[4] 102.0 5.68 89.56 114.4X[5] 62.0 5.839 49.39 74.88X[6] 140. 5.803 127.6 153.1X[7] -74.0 5.692 -86.53 -61.79X[8] -24.0 5.735 -36.48 -11.64X[9] -43.0 5.813 -55.5 -30.23X[10] -801.0 5.782 -813.6 -788.2

Electrostatic voltage sampling measurements, taking into account measurement error (standard).

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 P(X) sd 2.5% 97.5%X[1] 0.7275 0.0123 0.703 0.7511X[2] 0.0229 0.004157 0.01549 0.03174X[3] 0.0168 0.00354 0.01058 0.02426X[4] 0.07811 0.007419 0.06409 0.09317X[5] 0.04749 0.005876 0.03665 0.0598X[6] 0.1071 0.00855 0.09116 0.1246-V Points Sn[1] 0.07861 0.008738 0.06226 0.09634Sn[2] 0.02544 0.005165 0.01633 0.03636Sn[3] 0.0456 0.006798 0.03328 0.05967Sn[4] 0.8503 0.01161 0.8266 0.8724

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Analysis: Wafer Charge Example

• 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.

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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

ESD event distributions forcomparative peak amplitude canalso be characterized usingmultinomial probability distributions(in this case a Dirichlet distribution,which gives the probability forindividual measures for discretedistributions).

This can be of use in interferencemodeling and investigations.

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

X[7] 0.014 0.033

X[8] 0.019 0.041

X[9] 0.015 0.034

X[10] 0.021 0.042

X[11] 0.002 0.012

X[12] 0.015 0.035

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

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ESD Events by Frequency of Occurrence

A Poisson distribution gives the probability of occurrence atany time t for a stochastic event series. It is typically used tocalculate rate probabilities across time periods.

Test Period As % Prob sd 2.5% 97.5% Period[1] 11 0.1059 0.02983 0.0555 0.1716 Period[2] 24 0.2445 0.04464 0.1656 0.3394 Period[3] 18 0.1791 0.03884 0.1118 0.264 Period[4] 48 0.4832 0.06324 0.3674 0.6147 Period[5] 75 0.7554 0.07816 0.6107 0.9154

Time Period (minutes)

120 120 120 120 120

ESD Events(counts)

12 29 21 58 91

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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

• GLM (General Linear Regression Models)

• Multivariate Analysis

• MCMC (Markov Chain Monte Carlo)

• ANOVA

• Bayesian Network Analysis (BNAs)

• Log Odds Ratios for model comparison

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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