ISQED 2007Cho et al.

A Data-Driven Statistical Approach to Analyzing Process Variation in

65nm SOI Technology

Choongyeun Cho1, Daeik Kim1, Jonghae Kim1, Jean-Olivier Plouchart1, Daihyun Lim2,

Sangyeun Cho3, and Robert Trzcinski1

1IBM, 2MIT, 3U. of Pittsburgh

ISQED 2007, San Jose, Mar 28, 2007

Final

2ISQED 2007Cho et al.

Outline Introduction

Motivation of this work Constrained Principal Component Analysis Proposed method

Experiments Using 65nm SOI technology

Conclusion Applications, future work Contributions

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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

4ISQED 2007Cho et al.

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

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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.

6ISQED 2007Cho et al.

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:

w1 = arg maxjjw jj=1

var(wT x)

wherex is an original vector and wi is i-th PC.

wk = arg maxjjw jj=1;w? w i 8i=1;:::;k¡ 1

var(wT x);k ¸ 2

x

y

PC1PC2

7ISQED 2007Cho et al.

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

W2WW2W

D2D

D2D

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Proposed Algorithm

Standardize

In-line data

Screen data

Find first PCfor D2D variation

Find first PCfor W2W variation

Take PCwith larger variance

Subtract this PCspace from

original data

Can generalize for within-die and lot-to-lot variations.

Implemented with <100 lines of Matlab code.

9ISQED 2007Cho et al.

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

FET RO SRAM Capacitors Total

Before screen 1988 248 398 222 2856

After screen 759 83 159 108 1109

10ISQED 2007Cho et al.

1 5 10 15 200.2

0.3

0.4

0.5

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0.8

PC/CPC Index

Cu

mu

lati

ve n

orm

. var

ian

ce e

xpla

ined

PCA

CPC Index

TypeVariance explained

Cumulative Variance explained

1 D2D 31.0% 31.0%

2 W2W 25.2% 56.2%

3 D2D 4.5% 60.7%

4 W2W 4.2% 64.9%

Constrained PCA

Case I: 65nm SOI Tech

Δ

Die-Wafer Interaction

D2D

W2W

D2D

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Case I: 65nm SOI Tech

-60

-40

-20

0

20

40

0 5 10 15

-20

-10

0

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Wafer

Sys

tem

atic

var

iati

on

2nd CPC4th CPC5th CPC

D2D variation (1st CPC)

(Fitted with 2nd order polynomials on the 40 available samples)

W2W variations

(2nd,4th,5th CPC’s)

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WaferSite

Fo

sc

Case II: Applied to RF Circuit

Die index

Fo

sc

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:

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Fo

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WaferSite

Reconstruction 1

Offset

Die index

Fo

sc

Wafer index

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WaferSite

Fo

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Reconstruction 2

Offset + CPC#1 (D2D)

Die index

Fo

sc

Wafer index

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WaferSite

Fo

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Reconstruction 3

Offset + CPC#1 + CPC#2 (W2W)

Die index

Fo

sc

Wafer index

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WaferSite

Fo

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Reconstruction 4

Offset + CPC#1 + CPC#2 + CPC#3 (D2D)

Die index

Fo

sc

Wafer index

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WaferSite

Fo

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Reconstruction 5

Offset + CPC#1 + CPC#2 + CPC#3 + CPC#4 (W2W)

Die index

Fo

sc

Wafer index

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WaferSite

Fo

sc

Reconstruction & Original PVs obtained from in-line measurement explain significant

portion (66%) of PV existing in complex RF circuit.

Die index

Fo

sc

Wafer index

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Iteration 1 (Pre-production)

Iteration 2 Iteration 3

Case III: Technology Monitoring

Dominant D2D variations obtained for three successive 65nm SOI tech iterations. Visualize how technology stabilizes.

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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.

21ISQED 2007Cho et al.

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.

22ISQED 2007Cho et al.

Thanks!Q & A