ISQED 2007 Cho 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
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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 Cho 1 , Daeik Kim 1 , Jonghae Kim 1 , Jean-Olivier Plouchart 1 , Daihyun Lim 2 , Sangyeun Cho 3 , and Robert Trzcinski 1. - PowerPoint PPT Presentation
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ISQED 2007Cho et al.
A Data-Driven Statistical Approach to Analyzing Process Variation in
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
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0 5 10 15
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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
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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.
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Fosc
WaferSite
Reconstruction 1
Offset
Die index
Fosc
Wafer index
14ISQED 2007Cho et al.
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WaferSite
Fosc
Reconstruction 2
Offset + CPC#1 (D2D)
Die index
Fosc
Wafer index
15ISQED 2007Cho et al.
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WaferSite
Fosc
Reconstruction 3
Offset + CPC#1 + CPC#2 (W2W)
Die index
Fosc
Wafer index
16ISQED 2007Cho et al.
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WaferSite
Fosc
Reconstruction 4
Offset + CPC#1 + CPC#2 + CPC#3 (D2D)
Die index
Fosc
Wafer index
17ISQED 2007Cho et al.
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WaferSite
Fosc
Reconstruction 5
Offset + CPC#1 + CPC#2 + CPC#3 + CPC#4 (W2W)
Die index
Fosc
Wafer index
18ISQED 2007Cho et al.
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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.