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

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

3ISQED 2007Cho et al.

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 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

5ISQED 2007Cho et al.

What is In-line Data? In this work, “in-line” data refers to:

Electrical measurements in manufacturing line using a parametric tester for various purposes: fault diagnosis, device dc characterization, and model-hardware correlation (MHC).

Thus, available very early in the manufacturing process.

Key PV parameters (VT, LPOLY, TOX, etc) are mostly embedded in in-line data yet in an obscure manner.

We statistically exploit in-line data to extract D2D and W2W variations individually.

6ISQED 2007Cho et al.

Principal Component Analysis Principal Component Analysis (PCA)

rotates coordinates such that resulting vectors are: Uncorrelated, Ordered in terms of variance.

Can be defined recursively:w1 = arg max

jjw jj=1var(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

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 a PC must align

with D2D or W2W variation direction.

Ordinary PCA

Proposed CPCA

8ISQED 2007Cho et al.

Proposed Algorithm

Standardization

In-line data

Screening

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 was <1min on

an ordinary PC.

Type FET RO SRAM Capacitance Total

# Param’s 759 83 159 108 1109

10ISQED 2007Cho et al.

1 5 10 15 200.2

0.3

0.4

0.5

0.6

0.7

0.8

PC/CPC Index

Cum

ulat

ive

varia

nce

expl

aine

d

PCA

CPC Index Type Variance

explained

Cumulative Variance explained

1 Die 31.0% 31.0%2 Wafer 25.2% 56.2%3 Die 4.5% 60.7%4 Wafer 4.2% 64.9%5 Wafer 2.4% 67.3%

Constrained PCA

Case I: 65nm SOI Tech

11ISQED 2007Cho et al.

Case I: 65nm SOI Tech

-60

-40

-20

0

20

40

0 5 10 15

-20

-10

0

10

20

30

Wafer

Syst

emat

ic v

aria

tion

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)

12ISQED 2007Cho et al.

Original

05

10

0

20

4025

30

35

40

45

WaferSite

Fosc

Case II: Applied to RF Circuit

Die index

Fosc

Wafer index

Bench-tested RF self-oscillation frequencies (Fosc) for static CML frequency divider.

13ISQED 2007Cho et al.

05

10

0

20

4025

30

35

40

45

Fosc

WaferSite

Reconstruction 1

Offset

Die index

Fosc

Wafer index

14ISQED 2007Cho et al.

05

10

0

20

4025

30

35

40

45

WaferSite

Fosc

Reconstruction 2

Offset + CPC#1 (D2D)

Die index

Fosc

Wafer index

15ISQED 2007Cho et al.

05

10

0

20

4025

30

35

40

45

WaferSite

Fosc

Reconstruction 3

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

Die index

Fosc

Wafer index

16ISQED 2007Cho et al.

05

10

0

20

4025

30

35

40

45

WaferSite

Fosc

Reconstruction 4

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

Die index

Fosc

Wafer index

17ISQED 2007Cho et al.

05

10

0

20

4025

30

35

40

45

WaferSite

Fosc

Reconstruction 5

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

Die index

Fosc

Wafer index

18ISQED 2007Cho et al.

05

10

0

20

4025

30

35

40

45

WaferSite

Fosc

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

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

Die index

Fosc

Wafer index

19ISQED 2007Cho et al.

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.

20ISQED 2007Cho et al.

Application / Future Work Intelligent sampling: D2D variation

signature may serve as a guideline to pick representative chips for sampled tests.

Technology snapshot: Use D2D variation to monitor characteristic of a given lot or technology.

Future work includes: Incorporate within-die and lot-to-lot variations. Statistical elaboration (Non-Gaussianity, etc).

21ISQED 2007Cho et al.

Contributions 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.

Verified that RF circuit performance is tied to device PV’s.