Circuit Analysis and Defect Characteristics Estimation ... fileCircuit Analysis and Defect...
Transcript of Circuit Analysis and Defect Characteristics Estimation ... fileCircuit Analysis and Defect...
Circuit Analysis and Defect Characteristics Estimation
Method Using Bimodal Defect-Centric
Random Telegraph Noise Model
March 17, 2016
TAU 2017
Michitarou Yabuuchi (Renesas System Design Co., Ltd.),
Azusa Oshima, Takuya Komawaki, Ryo Kishida,
Jun Furuta, Kazutoshi Kobayashi (Kyoto Inst. of Tech.),
Pieter Weckx (KU Leuven, IMEC), Ben Kaczer (IMEC),
Takashi Matsumoto (University of Tokyo), and
Hidetoshi Onodera (Kyoto University) 1
Kyoto Inst. of Tech.
Summary
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ฮคโ๐น ๐นmax ฮคโ๐น ๐นmax
๐ ๐
Measurement result of
frequency fluctuation
distribution by RTN
RTN Prediction by
proposed method
Defect parameter extraction method and
RTN (random telegraph noise) prediction method
What is proposed?
@40 nm
SiON
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Contents
Introduction
Measurement of RTN
Parameter extraction method
Result
Conclusion
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Variation on scaled process
RTN affects the yields
โ CMOS image sensor
โ Flash, SRAM
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process voltage temperature
process voltage temperature RTN
-65 nm
40 nm-
scaling More significant
in โsmall areaโ
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RTN: Random Telegraph Noise
โ๐th /defect
5Si
t
|โ๐ th|
+ +
+
++
+
++
Carier
Capture Emit
Gate area
๐ฟ๐
# of defect
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Threshold voltage shift ฮ๐th by RTN
Defect-centric distribution
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# of Defect ๐ โ ๐ฟ๐
Poisson dist.
ฮ๐th /defect ๐ โ1
๐ฟ๐
Exponential dist.
Avg. ๐โ๐th = ๐ ร ๐
Std. dev. ๐ฮ๐th = 2๐๐2 โ ฮค1 ๐ฟ๐
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RTN in high-k process
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๏ฝ65nm 40nm 28nm
Unimodal model Bimodal model
Each oxide layer has its parameters
High-k layer (HK) :๐ต๐๐, ๐ผ๐๐Interface layer (IL) :๐ต๐๐, ๐ผ๐๐
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CC
DFร
N
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Unimodal model
(N, ๐ผ)
SiO2 or SiON HKMG
Bimodal model
(NHK, ๐ผHK, NIL, ๐ผIL)
thin HK/IL
CC
DFร
N
ฮVth [ mV] ฮVth [ mV]
Comparison : Unimodal vs Bimodal
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Calculation by bimodal model
of Defect-centric distribution
Circuit-level RTN prediction
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Defect
parameter
Threshold
voltage shift
Netlist
w/ โ๐th
RTN
predictionCircuit
Monte-Carlo circuit simulation
๐ต๐๐, ๐ผ๐๐, ๐ต๐๐, ๐ผ๐๐ ?
Kyoto Inst. of Tech.
Purpose of this study
Parameter extraction method for RTN characteristics
of bimodal model of Defect-centric distribution
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Defect
parameter
Threshold
voltage shift
Netlist
w/ โ๐th
RTN
predictionCircuit
๐ต๐๐, ๐ผ๐๐, ๐ต๐๐, ๐ผ๐๐ !
RO measurement data
Proposed
method
Confirm w/
measured data
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Measurement circuit
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40 nm HK/Poly-Si Process
x840TEG
7-stage ring oscillator (RO)
Count # of oscillation by
using on-chip counter
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Measurement method
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ฮ๐น
๐นmax=๐นmax โ ๐นmin
๐นmaxCalculate for each RO
Conditions
9,024 times/RO
๐dd = 0.65 V
ฮ๐ก = 2.2 ms
๐กtotal = 20 s
Fmin
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Result of frequency fluctuation distribution by RTN
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Sta
ndard
norm
al quantile
ฮคโ๐น ๐นmax
8.61%840 ROs
Follow bimodal defect-centric distribution
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ฮคโ๐น ๐นmax
๐
Measured data
๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐
๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐
Optimize defect vector
ฮคโ๐น ๐นmax
๐
Prediction
How to extract parameters
KS test (calculate
object function)
Prior to the loop
Sensitivity Analysis
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Obtain threshold voltage shift
Calculate ฮ๐th w/ defect characteristicsโ By using defect-centric distribution
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๐ต๐๐,๐, ๐ผ๐๐,๐, ๐ต๐๐,๐, ๐ผ๐๐,๐
ฮ๐thp1
ฮ๐thn1
ฮ๐thp2
ฮ๐thn2
ฮ๐thp7
ฮ๐thn7
ใป ใป ใป
14 Tr. X 840 RO
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Convert ฮ๐th to frequency shift (1)
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ฮ๐th [V]
ฮคโ๐น
๐น max
PMOS
NMOS
Prior to the loop
Analyze sensitivity ฮ๐th to ฮคโ๐น ๐นmax of MOSFET
โ Simulation condition : same as measurement
โ Shift ฮ๐th of single NMOS and PMOS
๐n
๐p
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Convert ฮ๐th to frequency shift (2)
Calculate ฮคโ๐น ๐นmax with sensitivities ๐n, ๐p
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ฮ๐thp,๐ ร ๐p
ฮ๐thn,๐ ร ๐n
+
=
ฮคโ๐นINV,๐ ๐นmax
INV
ฮคโ๐น ๐นmax = ฮคโ๐นINV,๐ ๐นmax
RO
X840 RO
= prediction of ฮคโ๐น ๐นmax
distribution
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Calculation of object function
Kolmogorov-Smirnov test for null hypothesis
โpopulations of two samples are the same.โ
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ฮคโ๐น ๐นmax ฮคโ๐น ๐นmax
๐ ๐
Object function ๐ becomes larger when difference
b/w two CDF plots becomes smaller.
Sample #1:measured data Sample #2:prediction
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Manipulation of defect vector
Downhill simplex method
Solution for optimization problemโ Maximize object function ๐
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๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐
๐ต๐๐๐, ๐ผ๐๐๐, ๐ต๐๐๐, ๐ผ๐๐๐
๐๐
๐๐
๐๐
๐๐
Convergence condition ๐๐ > 0.99 or ๐MAX = 500
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Prediction vs measurement data
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Sta
ndard
Norm
al Q
uantile
ฮคโ๐น ๐นmax
Prediction
Measured
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Conclusion
RTN prediction method by using circuit
simulation with bimodal defect-centric
distribution
Parameter extraction method for defect
characteristics of bimodal model by
measurement data
Replicate circuit-level RTN effect by Monte-
Carlo simulation
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