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
2
Ξ€βπΉ πΉmax Ξ€βπΉ πΉmax
π π
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
Kyoto Inst. of Tech.
Contents
Introduction
Measurement of RTN
Parameter extraction method
Result
Conclusion
3
Kyoto Inst. of Tech.
Variation on scaled process
RTN affects the yields
β CMOS image sensor
β Flash, SRAM
4
process voltage temperature
process voltage temperature RTN
-65 nm
40 nm-
scaling More significant
in βsmall areaβ
Kyoto Inst. of Tech.
RTN: Random Telegraph Noise
βπth /defect
5Si
t
|βπ th|
+ +
+
++
+
++
Carier
Capture Emit
Gate area
πΏπ
# of defect
Kyoto Inst. of Tech.
Threshold voltage shift Ξπth by RTN
Defect-centric distribution
6
# of Defect π β πΏπ
Poisson dist.
Ξπth /defect π β1
πΏπ
Exponential dist.
Avg. πβπth = π Γ π
Std. dev. πΞπth = 2ππ2 β Ξ€1 πΏπ
Kyoto Inst. of Tech.
RTN in high-k process
7
ο½65nm 40nm 28nm
Unimodal model Bimodal model
Each oxide layer has its parameters
High-k layer (HK) :π΅ππ, πΌππInterface layer (IL) :π΅ππ, πΌππ
Kyoto Inst. of Tech.
CC
DFΓ
N
8
Unimodal model
(N, πΌ)
SiO2 or SiON HKMG
Bimodal model
(NHK, πΌHK, NIL, πΌIL)
thin HK/IL
CC
DFΓ
N
ΞVth [ mV] ΞVth [ mV]
Comparison : Unimodal vs Bimodal
Kyoto Inst. of Tech.
Calculation by bimodal model
of Defect-centric distribution
Circuit-level RTN prediction
9
Defect
parameter
Threshold
voltage shift
Netlist
w/ βπth
RTN
predictionCircuit
Monte-Carlo circuit simulation
π΅ππ, πΌππ, π΅ππ, πΌππ ?
Kyoto Inst. of Tech.
Purpose of this study
Parameter extraction method for RTN characteristics
of bimodal model of Defect-centric distribution
10
Defect
parameter
Threshold
voltage shift
Netlist
w/ βπth
RTN
predictionCircuit
π΅ππ, πΌππ, π΅ππ, πΌππ !
RO measurement data
Proposed
method
Confirm w/
measured data
Kyoto Inst. of Tech.
Measurement circuit
11
40 nm HK/Poly-Si Process
x840TEG
7-stage ring oscillator (RO)
Count # of oscillation by
using on-chip counter
Kyoto Inst. of Tech.
Measurement method
12
ΞπΉ
πΉmax=πΉmax β πΉmin
πΉmaxCalculate for each RO
Conditions
9,024 times/RO
πdd = 0.65 V
Ξπ‘ = 2.2 ms
π‘total = 20 s
Fmin
Kyoto Inst. of Tech.
Result of frequency fluctuation distribution by RTN
13
Sta
ndard
norm
al quantile
Ξ€βπΉ πΉmax
8.61%840 ROs
Follow bimodal defect-centric distribution
Kyoto Inst. of Tech.
14
Ξ€βπΉ πΉmax
π
Measured data
π΅πππ, πΌπππ, π΅πππ, πΌππππ΅πππ, πΌπππ, π΅πππ, πΌππππ΅πππ, πΌπππ, π΅πππ, πΌπππ
π΅πππ, πΌπππ, π΅πππ, πΌπππ
Optimize defect vector
Ξ€βπΉ πΉmax
π
Prediction
How to extract parameters
KS test (calculate
object function)
Prior to the loop
Sensitivity Analysis
Kyoto Inst. of Tech.
Obtain threshold voltage shift
Calculate Ξπth w/ defect characteristicsβ By using defect-centric distribution
15
π΅ππ,π, πΌππ,π, π΅ππ,π, πΌππ,π
Ξπthp1
Ξπthn1
Ξπthp2
Ξπthn2
Ξπthp7
Ξπthn7
γ» γ» γ»
14 Tr. X 840 RO
Kyoto Inst. of Tech.
Convert Ξπth to frequency shift (1)
16
Ξπth [V]
Ξ€βπΉ
πΉ max
PMOS
NMOS
Prior to the loop
Analyze sensitivity Ξπth to Ξ€βπΉ πΉmax of MOSFET
β Simulation condition : same as measurement
β Shift Ξπth of single NMOS and PMOS
πn
πp
Kyoto Inst. of Tech.
Convert Ξπth to frequency shift (2)
Calculate Ξ€βπΉ πΉmax with sensitivities πn, πp
17
Ξπthp,π Γ πp
Ξπthn,π Γ πn
+
=
Ξ€βπΉINV,π πΉmax
INV
Ξ€βπΉ πΉmax = Ξ€βπΉINV,π πΉmax
RO
X840 RO
= prediction of Ξ€βπΉ πΉmax
distribution
Kyoto Inst. of Tech.
Calculation of object function
Kolmogorov-Smirnov test for null hypothesis
βpopulations of two samples are the same.β
18
Ξ€βπΉ πΉmax Ξ€βπΉ πΉmax
π π
Object function π becomes larger when difference
b/w two CDF plots becomes smaller.
Sample #1:measured data Sample #2:prediction
Kyoto Inst. of Tech.
Manipulation of defect vector
Downhill simplex method
Solution for optimization problemβ Maximize object function π
19
π΅πππ, πΌπππ, π΅πππ, πΌππππ΅πππ, πΌπππ, π΅πππ, πΌππππ΅πππ, πΌπππ, π΅πππ, πΌπππ
π΅πππ, πΌπππ, π΅πππ, πΌπππ
ππ
ππ
ππ
ππ
Convergence condition ππ > 0.99 or πMAX = 500
Kyoto Inst. of Tech.
Prediction vs measurement data
20
Sta
ndard
Norm
al Q
uantile
Ξ€βπΉ πΉmax
Prediction
Measured
Kyoto Inst. of Tech.
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
21