A Data-Driven Statistical Approach to Analyzing Process Variation in 65nm SOI Technology

A Data-Driven Statistical Approach to Analyzing Process Variation in 65nm SOI Technology ISQED 2007, San Jose, Mar 28, 2007 Choongyeun Cho1, Daeik Kim1, Jonghae Kim1, Jean-Olivier Plouchart1, Daihyun Lim2, Sangyeun Cho3, and Robert Trzcinski1 1IBM, 2MIT, 3U. of Pittsburgh Final

Outline • Introduction • Motivation of this work • Constrained Principal Component Analysis • Proposed method • Experiments • Using 65nm SOI technology • Conclusion • Applications, future work • Contributions

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-die Die-to-Die Wafer-to-Wafer Lot-to-Lot

Motivation • We present an efficient method to decompose PV into D2D and W2W components. • Use existing manufacturing “in-line” data only. • No model! Within-die Die-to-Die Wafer-to-Wafer Lot-to-Lot

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 (VT, LPOLY, TOX, 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.

h l d h P C i i i i i T T t t ( ( ) ) k x w w e r e s a n o r g n a v e c o r a n s - 2 ¸ i w w w x w x a r g a r m g a x m a x v a r v a r = = k 1 . ; j j j j j j j j ? 8 k i 1 1 1 1 ¡ w w w w = = = i ; ; : : : ; 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: y PC2 PC1 x

Ordinary PCA Proposed CPCA 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. D2D D2D W2W W2W

Proposed Algorithm In-line data • Can generalize for within-die and lot-to-lot variations. • Implemented with <100 lines of Matlab code. Standardize 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

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.

Case I: 65nm SOI Tech PCA 0.8 Δ 0.7 Die-Wafer Interaction Constrained PCA 0.6 D2D Cumulative norm. variance explained W2W 0.5 0.4 0.3 D2D 0.2 1 5 10 15 20 PC/CPC Index

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

45 40 35 Fosc 30 25 40 10 20 5 0 0 Site Wafer Case II: Applied to RF Circuit • 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: Fosc Die index Wafer index

45 40 35 Fosc 30 25 40 10 20 5 0 0 Site Wafer Reconstruction 1 Fosc Die index Wafer index Offset

45 40 35 Fosc 30 25 40 10 20 5 0 0 Site Wafer Reconstruction 2 Fosc Die index Wafer index Offset + CPC#1 (D2D)

45 40 35 Fosc 30 25 40 10 20 5 0 0 Site Wafer Reconstruction 3 Fosc Die index Wafer index Offset + CPC#1 + CPC#2 (W2W)

45 40 35 Fosc 30 25 40 10 20 5 0 0 Site Wafer Reconstruction 4 Fosc Die index Wafer index Offset + CPC#1 + CPC#2 + CPC#3 (D2D)

45 40 35 Fosc 30 25 40 10 20 5 0 0 Site Wafer Reconstruction 5 Fosc Die index Wafer index Offset + CPC#1 + CPC#2 + CPC#3 + CPC#4 (W2W)

45 40 35 Fosc 30 25 40 10 20 5 0 0 Site Wafer Reconstruction & Original • PVs obtained from in-line measurement explain significant portion (66%) of PV existing in complex RF circuit. Fosc Die index Wafer index

Case III: Technology Monitoring • Dominant D2D variations obtained for three successive 65nm SOI tech iterations. • Visualize how technology stabilizes. Iteration 1 (Pre-production) Iteration 2 Iteration 3

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.

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.

Thanks!Q & A

A Data-Driven Statistical Approach to Analyzing Process Variation in 65nm SOI Technology