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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. 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. 5 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. 6 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. 7 Measurement Tools Electrostatic Voltmeters Nanocoulomb meters Electrometers 8 Measurement Tools Oscilloscopes ESD Detectors Faraday Cups Electrostatic Field meters 9 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) . 14 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. 15 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. 16 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. 17 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] 18 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 19 • 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. 20 Derived Probability Densities Same event distribution viewed as a Gaussian* probability density. *Note tail 21 Multinomial Distributions by Frequency Data with non-Gaussian distributions can indicate multiple phenomena, states or sources. 22 Non-Gaussian Distributions Beware of inappropriate averaging (means). 23 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. 24 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] 25 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. 26 Some Analytical Methods 27 • 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 29