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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)

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Kyoto Inst. of Tech.

Summary

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Τ ∆𝐺 𝐺

max

Τ ∆𝐺 𝐺

max

𝜏 𝜏

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

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Kyoto Inst. of Tech.

Variation on scaled process

 RTN affects the yields

– CMOS image sensor – Flash, SRAM

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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

∆𝑊

th /defect

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Si t |∆𝑊

th|

+ + + + + + + + Carier

Capture Emit

Gate area 𝑀𝑋 # of defect

Kyoto Inst. of Tech.

Threshold voltage shift Δ𝑊

th by RTN

 Defect-centric distribution

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# of Defect 𝑂 ∝ 𝑀𝑋 Poisson dist. Δ𝑊

th /defect 𝜃 ∝ 1 𝑀𝑋

Exponential dist.

Avg. 𝜈∆𝑊th = 𝑂 × 𝜃

• Std. dev. 𝜏Δ𝑊th =

2𝑂𝜃2 ∝ Τ 1 𝑀𝑋

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) :𝑶𝐈𝐋, 𝜽𝐈𝐋 Interface layer (IL) :𝑶𝐉𝐌, 𝜽𝐉𝐌

Kyoto Inst. of Tech.

CCDF×N 8

Unimodal model (N, 𝜽)

SiO2 or SiON HKMG

Bimodal model (NHK, 𝜽HK, NIL, 𝜽IL)

thin HK/IL

CCDF×N

ΔVth [ mV] ΔVth [ mV]

Comparison : Unimodal vs Bimodal

Kyoto Inst. of Tech.

Calculation by bimodal model

• f Defect-centric distribution

Circuit-level RTN prediction

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Defect parameter Threshold voltage shift Netlist w/ ∆𝑊

th

RTN prediction

Circuit Monte-Carlo circuit simulation

𝑶𝐈𝐋, 𝜽𝐈𝐋, 𝑶𝐉𝐌, 𝜽𝐉𝐌 ?

Kyoto Inst. of Tech.

Purpose of this study

 Parameter extraction method for RTN characteristics

• f bimodal model of Defect-centric distribution

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Defect parameter Threshold voltage shift Netlist w/ ∆𝑊

th

RTN prediction

Circuit

𝑶𝐈𝐋, 𝜽𝐈𝐋, 𝑶𝐉𝐌, 𝜽𝐉𝐌 !

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 x840 TEG

7-stage ring oscillator (RO)

Count # of oscillation by using on-chip counter

Kyoto Inst. of Tech.

Measurement method

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Δ𝐺 𝐺

max

= 𝐺

max − 𝐺min

𝐺

max

Calculate for each RO Conditions 9,024 times/RO 𝑊

dd = 0.65 V

Δ𝑢 = 2.2 ms 𝑢total = 20 s

Fmin

Kyoto Inst. of Tech.

Result of frequency fluctuation distribution by RTN

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Standard normal quantile Τ ∆𝐺 𝐺

max

8.61%

840 ROs Follow bimodal defect-centric distribution

Kyoto Inst. of Tech.

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Τ ∆𝐺 𝐺

max

𝜏 Measured data

𝑶𝐈𝐋𝟒, 𝜽𝐈𝐋𝟒, 𝑶𝐉𝐌𝟒, 𝜽𝐉𝐌𝟒 𝑶𝐈𝐋𝟑, 𝜽𝐈𝐋𝟑, 𝑶𝐉𝐌𝟑, 𝜽𝐉𝐌𝟑 𝑶𝐈𝐋𝟐, 𝜽𝐈𝐋𝟐, 𝑶𝐉𝐌𝟐, 𝜽𝐉𝐌𝟐 𝑶𝐈𝐋𝟏, 𝜽𝐈𝐋𝟏, 𝑶𝐉𝐌𝟏, 𝜽𝐉𝐌𝟏 Optimize defect vector

Τ ∆𝐺 𝐺

max

𝜏 Prediction

How to extract parameters

KS test (calculate

• bject function)

Prior to the loop Sensitivity Analysis

Kyoto Inst. of Tech.

Obtain threshold voltage shift

 Calculate Δ𝑊

th w/ defect characteristics

– By using defect-centric distribution

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𝑶𝐈𝐋,𝒋, 𝜽𝐈𝐋,𝒋, 𝑶𝐉𝐌,𝒋, 𝜽𝐉𝐌,𝒋

Δ𝑊

thp1

Δ𝑊

thn1

Δ𝑊

thp2

Δ𝑊

thn2

Δ𝑊

thp7

Δ𝑊

thn7

・ ・ ・

14 Tr. X 840 RO

Kyoto Inst. of Tech.

Convert Δ𝑊

th to frequency shift (1)

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Δ𝑊

th [V]

Τ ∆𝐺 𝐺

max

PMOS NMOS

 Prior to the loop  Analyze sensitivity Δ𝑊

th to

Τ ∆𝐺 𝐺

max of MOSFET

– Simulation condition : same as measurement – Shift Δ𝑊

th of single NMOS and PMOS

𝑙n 𝑙p

Kyoto Inst. of Tech.

Convert Δ𝑊

th to frequency shift (2)

 Calculate

Τ ∆𝐺 𝐺

max with sensitivities 𝑙n, 𝑙p

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Δ𝑊

thp,𝑗 × 𝑙p

Δ𝑊

thn,𝑗 × 𝑙n

+ =

Τ ∆𝐺INV,𝑗 𝐺

max

INV Τ ∆𝐺 𝐺

max = ෍

Τ ∆𝐺INV,𝑗 𝐺

max

RO X840 RO = prediction of Τ ∆𝐺 𝐺

max

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 ∆𝐺 𝐺

max

Τ ∆𝐺 𝐺

max

𝜏 𝜏

Object function 𝑞 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 𝑞

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𝑶𝐈𝐋𝟒, 𝜽𝐈𝐋𝟒, 𝑶𝐉𝐌𝟒, 𝜽𝐉𝐌𝟒 𝑶𝐈𝐋𝟑, 𝜽𝐈𝐋𝟑, 𝑶𝐉𝐌𝟑, 𝜽𝐉𝐌𝟑 𝑶𝐈𝐋𝟐, 𝜽𝐈𝐋𝟐, 𝑶𝐉𝐌𝟐, 𝜽𝐉𝐌𝟐 𝑶𝐈𝐋𝟏, 𝜽𝐈𝐋𝟏, 𝑶𝐉𝐌𝟏, 𝜽𝐉𝐌𝟏 𝒒𝟏 𝒒𝟐 𝒒𝟑 𝒒𝒋 Convergence condition 𝑞𝑗 > 0.99 or 𝑗MAX = 500

Kyoto Inst. of Tech.

Prediction vs measurement data

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Standard Normal Quantile Τ ∆𝐺 𝐺

max

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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