1. ISQED 2007Cho et al. A Data-Driven Statistical Approach to Analyzing Process Variation in 65nm SOI Technology Choongyeun Cho 1, Daeik Kim 1, Jonghae Kim 1, Jean-Olivier Plouchart 1, Daihyun Lim 2, Sangyeun Cho 3, and Robert Trzcinski 1 1 IBM, 2 MIT, 3 U. of Pittsburgh ISQED 2007, San Jose, Mar 28, 2007 Final

2. ISQED 2007Cho et al. 2 Outline  Introduction  Motivation of this work  Constrained Principal Component Analysis  Proposed method  Experiments  Using 65nm SOI technology  Conclusion  Applications, future work  Contributions

3. ISQED 2007Cho et al. 3 Motivation  Process variation (PV) limits performance/yield of an IC.  PV is hard to model or predict.  Many factors of different nature contribute to PV.  Physical modeling is often intractable.  Four ranges of PV: Within-dieDie-to-DieWafer-to-WaferLot-to-Lot

4. ISQED 2007Cho et al. 4 Motivation  We present an efficient method to decompose PV into D2D and W2W components.  Use existing manufacturing “in-line” data only.  No model! Within-dieDie-to-DieWafer-to-WaferLot-to-Lot

5. ISQED 2007Cho et al. 5 What is In-line Data?  In this work, “in-line” data refers to:  Electrical measurements in manufacturing line for various purposes: fault diagnosis, device dc characterization, and model-hardware correlation. Test structures include: FET’s, ring oscillators, SRAM, etc.  Thus, available early in the manufacturing stage.  Key PV parameters (V T, L POLY, T OX, etc) are embedded in well chosen in-line data, yet in a complex manner especially for nanometer technologies.  We exploit statistics of in-line data to analyze and extract D2D and W2W variations separately.

6. ISQED 2007Cho et al. 6 Principal Component Analysis  Principal Component Analysis (PCA) rotates coordinates such that resulting vector is:  Uncorrelated, and  Ordered in terms of statistical variance.  Can be defined recursively: w 1 = argmax jj w jj = 1 var ( w T x ) w h ere x i sanor i g i na l vec t oran d w i i s i - t h PC. w k = argmax jj w jj = 1 ; w ? w i 8 i = 1 ;:::; k ¡ 1 var ( w T x ) ; k ¸ 2 x y PC1 PC2

7. ISQED 2007Cho et al. 7 Constrained PCA  Constrained PCA (CPCA): same as PCA except PC’s are constrained to a pre- defined subspace.  In this work, constraint is that every PC must align with D2D or W2W variation direction. Ordinary PCA Proposed CPCA W2W D2D

8. ISQED 2007Cho et al. 8 Proposed Algorithm Standardize In-line data Screen data Find first PC for D2D variation Find first PC for W2W variation Take PC with larger variance Subtract this PC space from original data  Can generalize for within-die and lot- to-lot variations.  Implemented with <100 lines of Matlab code.

9. ISQED 2007Cho et al. 9 Case I: 65nm SOI Tech  65nm SOI CMOS data (300mm wafer)  1109 in-line parameters used:  40 dies/wafer,13 wafers = 520 samples.  The run for whole data took <1min on an ordinary PC. Test structures FETROSRAMCapacitorsTotal Before screen19882483982222856 After screen759831591081109

10. ISQED 2007Cho et al. 10 15 1520 0.2 0.3 0.4 0.5 0.6 0.7 0.8 PC/CPC Index Cumulative norm. variance explained PCA CPC Index Type Variance explained Cumulative Variance explained 1D2D31.0% 2W2W25.2%56.2% 3D2D4.5%60.7% 4W2W4.2%64.9% Constrained PCA Case I: 65nm SOI Tech Δ Die-Wafer Interaction D2D W2W D2D

11. ISQED 2007Cho et al. 11 Case I: 65nm SOI Tech D2D variation (1 st CPC) (Fitted with 2nd order polynomials on the 40 available samples) W2W variations (2 nd,4 th,5 th CPC’s)

12. ISQED 2007Cho et al. 12 Case II: Applied to RF Circuit Die index Fosc Wafer index  This example shows how RF circuit variation can be expressed with device-level variation.  RF self-oscillation frequencies (Fosc) for a static CML frequency divider:

13. ISQED 2007Cho et al. 13 Reconstruction 1 Offset Die index Fosc Wafer index

14. ISQED 2007Cho et al. 14 Reconstruction 2 Offset + CPC#1 (D2D) Die index Fosc Wafer index

15. ISQED 2007Cho et al. 15 Reconstruction 3 Offset + CPC#1 + CPC#2 (W2W) Die index Fosc Wafer index

16. ISQED 2007Cho et al. 16 Reconstruction 4 Offset + CPC#1 + CPC#2 + CPC#3 (D2D) Die index Fosc Wafer index

17. ISQED 2007Cho et al. 17 Reconstruction 5 Offset + CPC#1 + CPC#2 + CPC#3 + CPC#4 (W2W) Die index Fosc Wafer index

18. ISQED 2007Cho et al. 18 Reconstruction & Original  PVs obtained from in-line measurement explain significant portion (66%) of PV existing in complex RF circuit. Die index Fosc Wafer index

19. ISQED 2007Cho et al. 19 Iteration 1 (Pre-production) Iteration 2Iteration 3 Case III: Technology Monitoring  Dominant D2D variations obtained for three successive 65nm SOI tech iterations.  Visualize how technology stabilizes.

20. ISQED 2007Cho et al. 20 Application / Future Work  Technology snapshot: Use D2D variation to monitor characteristic of a lot or technology iterations.  Intelligent sampling: D2D variation signature serves as a guideline to pick representative chips for sampled tests.  Future work includes:  Incorporate within-die and lot-to-lot variations.  Model-assisted constrained PC.

21. ISQED 2007Cho et al. 21 Conclusion  Presented a statistical method to separate die-to-die and wafer-to-wafer variations using PCA variant:  Allows visualization and analysis of systematic variations.  Rapid feedback to tech development.  Quantified how much RF circuit performance is tied to device PV’s.

22. ISQED 2007Cho et al. 22 Thanks! Q & A