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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Τ∆𝐹 𝐹max Τ∆𝐹 𝐹max

𝜎 𝜎

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

– CMOS image sensor

– Flash, SRAM

4

process voltage temperature

process voltage temperature RTN

-65 nm

40 nm-

scaling More significant

in “small area”

Kyoto Inst. of Tech.

RTN: Random Telegraph Noise

∆𝑉th /defect

5Si

t

|∆𝑉 th|

+ +

+

++

+

++

Carier

Capture Emit

Gate area

𝐿𝑊

# of defect

Kyoto Inst. of Tech.

Threshold voltage shift Δ𝑉th by RTN

Defect-centric distribution

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# of Defect 𝑁 ∝ 𝐿𝑊

Poisson dist.

Δ𝑉th /defect 𝜂 ∝1

𝐿𝑊

Exponential dist.

Avg. 𝜇∆𝑉th = 𝑁 × 𝜂

Std. dev. 𝜎Δ𝑉th = 2𝑁𝜂2 ∝ Τ1 𝐿𝑊

Kyoto Inst. of Tech.

RTN in high-k process

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～65nm 40nm 28nm

Unimodal model Bimodal model

Each oxide layer has its parameters

High-k layer (HK) :𝑵𝐇𝐊, 𝜼𝐇𝐊Interface layer (IL) :𝑵𝐈𝐋, 𝜼𝐈𝐋

Kyoto Inst. of Tech.

CC

DF×

N

8

Unimodal model

(N, 𝜼)

SiO2 or SiON HKMG

Bimodal model

(NHK, 𝜼HK, NIL, 𝜼IL)

thin HK/IL

CC

DF×

N

ΔVth [ mV] ΔVth [ 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/ ∆𝑉th

RTN

predictionCircuit

Monte-Carlo circuit simulation

𝑵𝐇𝐊, 𝜼𝐇𝐊, 𝑵𝐈𝐋, 𝜼𝐈𝐋 ?

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/ ∆𝑉th

RTN

predictionCircuit

𝑵𝐇𝐊, 𝜼𝐇𝐊, 𝑵𝐈𝐋, 𝜼𝐈𝐋 !

RO measurement data

Proposed

method

Confirm w/

measured data

Kyoto Inst. of Tech.

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

Kyoto Inst. of Tech.

Measurement method

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Δ𝐹

𝐹max=𝐹max − 𝐹min

𝐹maxCalculate for each RO

Conditions

9,024 times/RO

𝑉dd = 0.65 V

Δ𝑡 = 2.2 ms

𝑡total = 20 s

Fmin

Kyoto Inst. of Tech.

Result of frequency fluctuation distribution by RTN

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Sta

ndard

norm

al quantile

Τ∆𝐹 𝐹max

8.61%840 ROs

Follow bimodal defect-centric distribution

Kyoto Inst. of Tech.

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Τ∆𝐹 𝐹max

𝜎

Measured data

𝑵𝐇𝐊𝟑, 𝜼𝐇𝐊𝟑, 𝑵𝐈𝐋𝟑, 𝜼𝐈𝐋𝟑𝑵𝐇𝐊𝟐, 𝜼𝐇𝐊𝟐, 𝑵𝐈𝐋𝟐, 𝜼𝐈𝐋𝟐𝑵𝐇𝐊𝟏, 𝜼𝐇𝐊𝟏, 𝑵𝐈𝐋𝟏, 𝜼𝐈𝐋𝟏

𝑵𝐇𝐊𝟎, 𝜼𝐇𝐊𝟎, 𝑵𝐈𝐋𝟎, 𝜼𝐈𝐋𝟎

Optimize defect vector

Τ∆𝐹 𝐹max

𝜎

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 Δ𝑉th w/ defect characteristics– By using defect-centric distribution

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𝑵𝐇𝐊,𝒊, 𝜼𝐇𝐊,𝒊, 𝑵𝐈𝐋,𝒊, 𝜼𝐈𝐋,𝒊

Δ𝑉thp1

Δ𝑉thn1

Δ𝑉thp2

Δ𝑉thn2

Δ𝑉thp7

Δ𝑉thn7

・ ・ ・

14 Tr. X 840 RO

Kyoto Inst. of Tech.

Convert Δ𝑉th to frequency shift (1)

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Δ𝑉th [V]

Τ∆𝐹

𝐹 max

PMOS

NMOS

Prior to the loop

Analyze sensitivity Δ𝑉th to Τ∆𝐹 𝐹max of MOSFET

– Simulation condition : same as measurement

– Shift Δ𝑉th of single NMOS and PMOS

𝑘n

𝑘p

Kyoto Inst. of Tech.

Convert Δ𝑉th to frequency shift (2)

Calculate Τ∆𝐹 𝐹max with sensitivities 𝑘n, 𝑘p

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Δ𝑉thp,𝑖 × 𝑘p

Δ𝑉thn,𝑖 × 𝑘n

+

=

Τ∆𝐹INV,𝑖 𝐹max

INV

Τ∆𝐹 𝐹max = Τ∆𝐹INV,𝑖 𝐹max

RO

X840 RO

= prediction of Τ∆𝐹 𝐹max

distribution

Kyoto Inst. of Tech.

Calculation of object function

Kolmogorov-Smirnov test for null hypothesis

“populations of two samples are the same.”

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Τ∆𝐹 𝐹max Τ∆𝐹 𝐹max

𝜎 𝜎

Object function 𝑝 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 problem– Maximize object function 𝑝

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𝑵𝐇𝐊𝟑, 𝜼𝐇𝐊𝟑, 𝑵𝐈𝐋𝟑, 𝜼𝐈𝐋𝟑𝑵𝐇𝐊𝟐, 𝜼𝐇𝐊𝟐, 𝑵𝐈𝐋𝟐, 𝜼𝐈𝐋𝟐𝑵𝐇𝐊𝟏, 𝜼𝐇𝐊𝟏, 𝑵𝐈𝐋𝟏, 𝜼𝐈𝐋𝟏

𝑵𝐇𝐊𝟎, 𝜼𝐇𝐊𝟎, 𝑵𝐈𝐋𝟎, 𝜼𝐈𝐋𝟎

𝒑𝟎

𝒑𝟏

𝒑𝟐

𝒑𝒊

Convergence condition 𝑝𝑖 > 0.99 or 𝑖MAX = 500

Kyoto Inst. of Tech.

Prediction vs measurement data

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Sta

ndard

Norm

al Q

uantile

Τ∆𝐹 𝐹max

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

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