<Insert Picture Here> Inter-Dependence of Dielectric and Conductive Losses in Interconnects

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1 <Insert Picture Here> Inter-Dependence of Dielectric and Conductive Losses in Interconnects Gustavo J. Blando

2 It all started in 9. We just wanted to measure the loss tangent!!!! THE ELEPHANT 1Hz to 1MHz Range 1MHz to 1GHz range 1GHz point Industry Trend tand Pressed stack loss measurement methods: Rely on a combination of models and measurements to extract losses. In particular when conductor/dielectric loss separation is required [Hinckley, et al., Introduction and Comparison of an Alternate Methodology for Measuring Loss Tangent of PCB Laminates, DesignCon1, Santa Clara, CA, February 1-4, 1 f

3 A Simple Test Case By adjusting one of the parameters a perfect match can be obtained, even for very different loss tangent profiles As a minimum, this begs two questions: 1. How correct are these models?. Good correlation against what? F [Hz] F [Hz] SPP Sarkar 1MHz Sarkar 1MHz Sarkar 1MHz Sarkar 1GHz Sarkar 1GHz Insertion Loss SPP SUN 1MHz SUN 1MHz SUN 1MHz SUN 1GHz SUN 1GHz F [Hz] 1MHz F [Hz] DF SPP SPP SUN Sarkar x Area difference between SPP and Sarkar model insertion loss Surface Intersection represents perfect matching MHz 1MHz 1MHz 1GHz 1GHz DF Surface Intersection represents perfect matching.5 RMS 1 x 1-6 3

4 Is It possible to DIRECTLY measure copper and dielectric losses on a pressed stack? (Without pre-assuming a model 4

5 Theory Is it theoretically possible? If we were able to extract RLGC from measurement, separation of conductive and dielectric losses is automatic!!!!!! ( ( z V dz z V d γ ( ( z I dz z I d γ ω ω γ c j g l j r y z + + ( ( 1 1 cosh( sinh( sinh( cosh( I V l D Zc l C l Zc B l A I V γ γ γ γ B Zc A a cosh( γ Telegraphers Equation Lossy Transmission Line ABCD 5 β α ω ω γ j c j g l j r y z ( ( ( ( c j g l j r y z Zc ω ω + + C Zc ω γ ω Im(, Re( z l z r Zc l j r z + ω γ ω Im( Re(, z c y g Zc c j g y + l γ We are still assuming the t-line works in a TEM or Quasi-TEM mode. The fundamental parameters we need to determine RLGC are: Propagation Constant and Characteristic Impedance g /( c df ω π Loss tangent

6 Proof of Concept (Simulated Test-Case-1 x 1-1 Generate Transmission line RLGC model Real[Ohms] 5 51 Zc - -4 Imag[Ohms] Att[Neper] PropDelay[sec] Convert to S-parameters CMP db Extract back RLGC Insertion-Loss Return-Loss R x G GENERATED CONVERTED x x 1-9 x L C x x

7 Interesting Applications on Simulated Data Explore the equivalent uniform RLGC parameters from a nonuniform 3-D structure. Lossless material with copper traces and perpendicular blades Does G and R change for different blade heights? This methodology can help us explore the inner working of structures G R 7

8 Let s try the Process on Measurements Any type of discontinuities have to be minimized Wafer probes: GSG-5um SOLT calibration (to the TIPS of the wafer probes Very small lead-in trace before the uniform piece of transmission line Bottom and top GND plane connected to minimize current path redistribution Four measurements per set were done, all on the SAME transmission line (long, long-reverse, and after cutting the same line we measured short and shortreverse 8

9 S-Parameter Measurements Two samples shown (RTF and VLP, at two lengths (short, long Very good insertion loss profile Reasonable return loss <-db up to GHz Insertion Loss Comparison RTF-d VLP-d RTF-r VLP-r x Return Loss Comparison RTFd[11] RTFr[] RTFd[] RTFr[11] 7. x Delay Comparison Return Loss Comparison RTF-d VLP-d RTF-r VLP-r VLPd[11] VLPr[] VLPd[] VLPr[11] x x 1 1 9

10 SO HOW DOES Zc LOOK!!! Real part of ZC [Ohms] Real part of ZC [Ohms] S-par Short Long Short Long 5 48 ABCD ABCD Zc B C Upslope trend, maybe inductive discontinuity ½ wave resonance (end discontinuities In general pretty good overall baseline value, and correct trend Clearly, in contrast with simulation data, even very clean measurements have other issues. Other effects, such as error-terms, need to be considered if we ever hope to extract Zc cleanly

11 Characteristic Impedance Extraction Methods Direct Inversion Method (shown previously Impedance Renormalization Error Model Calculation Maximum Identification Frequency Adjustment Extraction of propagation constant has been shown in previous publications. In this work we ll focus primarily on Characteristic Impedance (Zc. 11

12 Characteristic Impedance by Renormalization Theory Z Zc DUT Z Renormalization S[1,1] 4OHM 45OHM 5OHM 55OHM 6OHM b1 S b S 11 1 S S 1 a a 1 With respect to Z Renormalization S[1,] x 1 9 Reflections (at the load can be modified by mathematically changing Z. This is called impedance renormalization If Zc were known and used as the reference impedance, the reflection would be zero The method consist of doing a frequency dependent complex impedance renormalization to minimize the reflection on the curve OHM 45OHM 5OHM 55OHM 6OHM x 1 9 1

13 Characteristic Impedance by Renormalization Results We see that the improvement is minimal and likely due to the averaging of the algorithm. Two independent methods, similar results. Are we only measuring the transmission line? Real part of ZC [Ohms] 15 Imaginary part of ZC [Ohms] 65 6 Short Long 1 5 Short Long

14 Error matrix 1 Characteristic Impedance by Error Model Real DUT to be determined Error matrix E1 CHL E Error terms could be: - End physical discontinuities - Measurement repeatability - Instrument / Calibration errors - Instrument noise floor Measured DUT - Others? A Short B Ae 1 Be 1 1+ ze ye ze E A Long B Ce1 De 1 ye 1 By measuring two lines (long and short, the complex propagation constant can be easily extracted This is not sufficient to get Zc, something else is needed? N ( ABCD ye error _ matrix Zc long ( ABCD [( ] N 1 + N N ( N + 1 [ ] N1 N1 [ ( ] N N + ye N N N short

15 Error Model Validation By Simulations and Measurements Results Simulated Data Left: Smaller discontinuity: RLGCa.1,.3nH,.5fF,1e-5 RLGCb.,.1nH,.5fF,1e-5 Right: Bigger discontinuity 76 real(zl real(zo real(zfound imag(zl imag(zo imag(zfound real(zl real(zo real(zfound imag(zl imag(zo imag(zfound RLGCa.1,.3nH,5fF,1e-3 RLGCb.,.1nH,5fF,1e The extraction is trying to correct the behavior but is unable to remove all the peaks and valleys A Short B A Long B Measurement, Real(Zc Corrected Original Measured Data Measurement, Imag(Zc Corrected Original - More repetitive connection (SMA would work better but it would have to be done on different physical lines F[Hz] F[Hz] 15

16 Characteristic Impedance by Maximum Identification (1 ABCD Zc B C 15 Let s try to 1 understand where the dips are coming from. The maximums can be identified (away from sensitive areas Less # of points but enough to understand frequency dependency V ( z I ( z I ( z V I + + e + V Zc e γz e γz + γz + V I e e γz V Zc γz e γz abs(b abs(c real(zc real(b real(bfitted max x 1 1 B Sensitive location abs(b abs(c imag(zc B real(b real(bfitted max x

17 Characteristic Impedance by Maximum Identification ( The Characteristic Impedance information is solely contained in the Bmax, Cmax curves Maximums of B max(real(b max(imag(b max(real(c max(imag(c Maximums of C We can see how it almost averages the results. The maximum-only curve doesn t have peaks, but the shape is still very questionable x 1 1 Real(ZC Ohms Direct-Zc Full-fitted Only-max Ohms x Direct-Zc Full-fitted Only-maximums Imag(ZC

18 RLGC Results Characteristic Impedance by Maximum Identification RLGC seems 5 to be modified in a drastic way, simply -5 by picking -1 the maximum R/length R Direct-Zc Full-fitted Only-maximums values x 1 1 G/length R G Direct-Zc Full-fitted Only-maximums x 1 1 L/length C/length 3.7 x L Direct-Zc Full-fitted 3. Only-maximums x 1-1 C Direct-Zc 1. Full-fitted Only-maximums

19 Characteristic Impedance By Frequency Adjustment (1 Identify the maxima Interpolate to get the most likely maximum -6 Adjust each curve by half the x 1 difference 7 fmax(b - fmax(c (Peaks of -abs(b B,C -abs(b -abs(c RTF-SHORT VLP-SHORT x B max Interpolation B and C modified x 1 9 Bmodified Cmodified x

20 Characteristic Impedance By Frequency Adjustment ( This method cleans the curves very well Direct real(zc real1 Freq, real(zc Direct imag(zc real Freq, imag(zc imag1 imag SHORT-RTF Short-Line Direct real(zc Freq, real(zc real1 Direct imag(zc real Freq, imag(zc imag1 imag LONG-RTF Both, trends and the peaks are 8 corrected BUT, is this good enough for our ultimate goal??? (RLGC extraction SHORT-VLP Direct real(zc real1 Freq, real(zc real Direct imag(zc imag1 Freq, imag(zc imag LONG-VLP Direct real(zc real1 Freq, real(zc real Direct imag(zc imag1 Freq, imag(zc imag

21 RLGC Results Characteristic Impedance by Frequency Adjustments The curves looks reasonable but still very noisy 4 3 R tf r R tf r i R lp v R x L RTF VLP Let s push it further and 1 R lp v i extract the loss tangent from here x 1 9 G RTF VLP x C RTF VLP x

22 Loss Tangent Extraction Characteristic Impedance by Frequency Adjustments Even though we get a correct overall averaged trend, the results are noisy enough to mask any necessary details Loss Tangent, RTF vs. VLP RTF RTF-1 VLP VLP

23 So Where are we? Shown accurate S-parameter measurements Shown how to extract the Characteristic Impedance using several methods (Direct-Inversion, Impedance Renormalization, Maximum Identification, Frequency Adjustment Developed math to account for small end-discontinuities. Method works in simulations environment and it could be very useful to enhance our understanding of 3-D structures. Methods were found to be lacking when it came to working with actual lab measurements AND IT WAS THE TIME TO SUBMIT THE PAPER!!! 3

24 Let s take a step back Zc Calculation is sensitive to what? E1 S-Short E ABCD_LONG OR ZC sqrt(b/c Calculate Zc using error formulas E1 S-Long E ABCD_SHORT ZC sqrt(b/c How does Zc looks in terms of S- K + S11 Zc ( f parameters directly K S11 OR Calculate Complex Prop Constant Simulated Data Insertion-Loss Return-Loss -4 - Measured Compare:Converted Data SHORT LONG db x Freq x 1 9 4

25 Going Back To Measurements Ways to further improve measurements Remove lead-in and lead-out traces Get data from other experts in the industry, with different methodologies, calibration techniques, to see if we can get better data Somehow improve S11 noise margin against the unknown (VNA + Calibration noise floor Could it be that real structural effects on the transmission line are creating this behavior?, What about weave-effects? Get a measurements of a non-glass reinforced material 5

26 Removing Lead-in Lead-Out Measurements from the side can be performed, hence completely eliminating lead-in and lead-out traces Mechanically complex calibration to do in our set-up -1 - S1 S x 1 1 6

27 Getting Data from Other Experts Just to make sure we are not missing anything in our measurement methodology we wanted to compare the quality of our data to that of other industry experts Real (Zc Imag (Zc im mag(zc 8 6 imag(zc Different Calibration techniques, different VNAs, different labs, different users, SAME PROBLEM 7

28 Conclusion It is starting to look like the fundamental RLGC telegrapher equations may not be directly applied to measurements for the purpose of separating Dielectric vs. Conductive Losses BUT We are not yet convinced that this is not possible.. 8

29 Moving Forward Understand in further depth the error expected from the VNA VNA return loss noise floor VNA different calibration techniques Make sure the measurement artifact is not coming from real transmission line structural elements Measure non-glass-materials in different ways Measure simple coax semi-rigid cables with wafer-probes Improve measurement techniques by engaging with other industry experts Compare S-parameter measurements on equivalent samples 9

30 Acknowledgements Thanks to Scott McMorrow, Al Neves and Mike Resso for their support and S-parameter samples. 3

31 <Insert Picture Here> Q & A Thank You Gustavo Blando