Calibration Uncertainty Estimation. at the Wafer Level
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1 Calibration Uncertainty Estimation for the S-Parameter S Measurements at the Wafer Level A. Rumiantsev SUSS MicroTec Test Systems GmbH Sussstr. 1, Sacka, D-01561, Germany a.rumiantsev@ieee.org
2 Outline Motivation Error Sources Calibration Standards Calibration Procedures Uncertainty Analysis Methods Conclusion A. Rumiantsev 2
3 Motivation Everybody s dream: results with uncertainty budgets (error bars) A. Rumiantsev 3
4 Outline Motivation Error Sources Calibration Standards Calibration Procedures Uncertainty Analysis Methods Conclusion A. Rumiantsev 4
5 Error Sources Reflection or transmission measurement: r =S ii, t=s ij, i,j=1,2,3, Measurement results contain errors A. Rumiantsev 5
6 Error Sources Instability of the instrument and accessories Temperature drift Trace noise, etc.. Cable phase instability Contact repeatability (connections, probes) Non-ideal calibration standards Modeling and fabrication tolerances Calibration and error correction method A. Rumiantsev 6
7 Outline Motivation Error Sources Calibration Standards Calibration Procedures Uncertainty Analysis Methods Conclusion A. Rumiantsev 7
8 Calibration Standards Distributed (transmission): Dispersive Frequency limited (loop-back, etc) thru, lines Lumped (reflection): Not ideal Insufficiently modeled May not be symmetrical load open short A. Rumiantsev 8
9 Calibration Standards Fabrication tolerances: Dielectric properties Tolerances of the mask Metal thickness and form Contact tolerances: Positioning accuracy Repeatability Δ Contact resistance A. Rumiantsev 9
10 Outline Motivation Error Sources Calibration Standards Calibration Procedures Uncertainty Analysis Methods Conclusion A. Rumiantsev 10
11 SOLT calibration Calibration Procedures Requires fully known (or ideal) standards 10-Term error model Self-calibration algorithms TRL, LRM/LRM+, SOLR, QSOLT, RRMT+.. 7-Term error model Some standards can be partly known Recommended for the wafer-level A. Rumiantsev 11
12 Calibration Procedures Influence of transmission standards SOLT SOLR QSOLT TRL LRM RRMT THRU (4 terms) LINE (2 terms) RECIP. (1 terms) TERMS A. Rumiantsev 12
13 Calibration Procedures Influence of reflection (lumped) standards SOLT SOLR QSOLT TRL LRM RRMT OPEN (1 terms) SHORT (1 terms) LOAD (1 terms) REFLECT (1 terms) 2x 2x 2x 2x 2x 2x 2x 2x 2x TERMS A. Rumiantsev 13
14 Outline Motivation Error Sources Calibration Standards Calibration Procedures Uncertainty Analysis Methods Conclusion A. Rumiantsev 14
15 Uncertainty Analysis Methods 1. Analysis of calibration standards Statistical Analytical 2. Calibration comparison method Analysis with respect to the reference calibration 3. Measurement method Analysis with respect to the reference element Classical ripple-test Wafer-level implementation if the ripple-test A. Rumiantsev 15
16 Ad 1.: Analysis of Calibration Standards Statistical analysis Specify uncertainty of standards Run simulation (i.e. Monte-Carlo) Apply results to the calibration procedure Analytical analysis δs XY.DUT from deviations of error terms δet IJ δet IJ from deviations of standards δs ST.XY A. Rumiantsev 16
17 Ad 2.: Calibration Comparison Method Requires two calibrations: Reference (well-known) Test Addresses variations in: Calibration standards Calibration methods Measurement setup (drift) Results: Max. error bounds A. Rumiantsev 17
18 Ad 2.: Calibration Comparison Method Block-diagram representation [A] REF [B] Test Calibration Reference Calibration Test Calibration [A] and [B] quantitatively describe the difference in Test and Reference calibration A. Rumiantsev 18
19 Ad 2.: Calibration Comparison Method Example: verification of the system integrity* Max Sij-S'ij FBH Instrument Drift NIST Instrument Drift Sum of FBH and NIST Drifts Measurement Deviations Frequency (GHz) *NIST Verify Program A. Rumiantsev 19
20 Ad 2.: Calibration Comparison Method Analysis of different coplanar calibrations A. Rumiantsev 20 SUSS, 2007
21 Ad 3.: Reference Measurements Reference element (coaxial applications): Air-isolated lines Well-defined characteristics: Z 0, αl, βl Wafer-level equivalent? Picture source: NPL A. Rumiantsev 21
22 Ad 3.: Reference Measurements Reference measurements (ripple-test): line, loaded with the short All errors are included in the final Source Match (as error vector r q ) Setup for the r q - calculation (ripple test) A. Rumiantsev 22
23 Classical Ripple Test Perfect VNA : Z 0 = Z q Real VNA : Z 0 Z q A. Rumiantsev 23
24 Wafer-Level Implementation Wafer-level challenge: Fabrication tolerances reduce accuracy Reference (planar) line is dispersive Solution: I. Line characterization (e.g. NIST methods) II. Renormalization from/to the line Z 0 A. Rumiantsev 24
25 Ad I: Characterization of Commercial CPW Measurement of the line s C Definition of the line s propagation constant γ (multiline TRL)* Calculation of the line s Z 0: *Available from MultiCal software package, NIST Z 0 γ jωc A. Rumiantsev 25
26 Ad I: Characterization of Commercial CPW Measurement results 55 Re(Zo), Ohm Sub A Sub B CSR Frequency (GHz) A. Rumiantsev 26
27 Ad II: Renormalization Return loss of the reference line Ohm Renormalized S11, (db) Frequency (GHz) Automated ripple-test can be applied A. Rumiantsev 27
28 Uncertainty Estimation: LRM+ Calibration Measurement results of a 25Ω resistor Ω CPW Resistor S11, (db) Frequency, (GHz) A. Rumiantsev 28
29 Uncertainty Estimation: LRM+ Calibration Measurement results of a 25Ω resistor Arg(S11), (degree) Ω CPW Resistor Frequency, (GHz) A. Rumiantsev 29
30 Outline Motivation Error Sources Calibration Standards Calibration Procedures Uncertainty Analysis Methods Conclusion A. Rumiantsev 30
31 Conclusion Multiple sources of calibration errors Different analysis methods are available Characterized CPW lines can be used as reference elements Results of the automated wafer-level ripple-test were demonstrated A. Rumiantsev 31
32 References European co-operation for Accreditation, Expression of the Uncertainty of Measurement in Calibration, EA-4/02, Eul, H.J., Schiek, B., A Generalized Theory and New Calibration Procedures for Network Analyzer Self-Calibration, IEEE Trans. Microwave Theory Tech., MTT-39, Apr. 1991, pp Heuermann, H., Schiek, B., Robust Algorithms for Txx Network Analyzer Procedures, IEEE Trans. Instrum. Meas., Feb. 1994, pp Marks, R., Williams, D., Characteristic Impedance Determination Using Propagation Constant Measurements, IEEE Microwave and Guided Wave Lett., vol. 1, pp , June A. Rumiantsev, H. Heuermann, S. Schott, A Robust Broadband Calibration Method for Wafer- Level Characterization of Multiport Devices, 69 th ARFTG Conference Digest, June 2007 Rumiantsev, A., Doerner, R., Thies, S., Calibration Standards Verification Procedure Using the Calibration Comparison Technique, 36 th European Microwave Conference Digest, September U. Arz, Traceability for On-Wafer S-Parameter Measurements, Workshop Determining Accuracy of Measurements at High Frequencies from Error to Uncertainty, 37th European Microwave Conference, R. Doerner, "Evaluation of wafer-level LRRM and LRM+ calibration techniques," ARFTG Microwave Measurements Conference-Spring, 69th, A. Rumiantsev 32
33 References (cont.) J. P. Hoffmann, P. Leuchtmann, J. Schaub, and R. Vahldieck, "Computing uncertainties of S- parameters by means of monte carlo simulation," in ARFTG Microwave Measurements Conference-Fall, 69 th, 2007 N. M. Ridler, A. G. Morgan, and M. J. Sadler, "Generalized adaptive calibration schemes for RF network analyzers based on minimizing the uncertainty of measurement, ARFTG Microwave Measurements Conference-Digest-Fall, 60th, 2002, pp U. Stumper, "Influence of TMSO calibration standards uncertainties on VNA S-parameter measurements," Instrumentation and Measurement, IEEE Transactions on, vol. 52, pp , U. Stumper, "Uncertainties of VNA S-parameter measurements applying the TAN selfcalibration method," Instrumentation and Measurement, IEEE Transactions on, vol. 56, pp , RF & Microwave Test Solutions, SUSS MicroTec Test Systems GmbH, Heuermann, H., Old and New Accuracy Estimation of S-Parameter Measurements with the Ripple-Test, MTT-S International Microwave Symposium Workshop TMB, San Francisco, Juni H. Heuermann and A. Rumiantsev, "The modified ripple test for on-wafer S-parameter measurements," ARFTG Microwave Measurements Conference-Spring, 69th, A. Rumiantsev 33
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