© Estoril – 19 September 2003 Advanced Compact Modeling Workshop MOSFETs Flicker Noise Modeling...

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

MOSFETs Flicker Noise Modeling For Circuit

Simulation

Montpellier University

A. Laigle, F. Martinez , A. Hoffmann and M. Valenza

valenza@cem2.univ-montp2.fr

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Outline

• Introduction

• Methodology and Instrumentation

• 1/f modeling– 1/f theory– 1/f models

• Experimental results

• Conclusion

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Introduction (1)

Low frequency noise is important for :

Conduction phenomena and random noise- White noise (thermal & shot noise)- 1/f and origin (N, µ, N- µ); RTS & G.R.- High electric field : multiplication- Correlation between two noise sources

Technologies evaluation - Reliability, quality, aging - Parasitic elements, defects

- Equivalent circuit

Analog applications with mixed CMOS technologies (LN amplifiers, oscillators, sensors …)

We need models

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Introduction (2)

t (ms)-10 -8 -6 -4 -2 0 2 4 6 8 10

I (µ

A)

-3

-2

-1

0

1

2

3

4

f (Hz)100 101 102 103 104 105

Si (

A²/

Hz)

10-25

10-24

10-23

10-22

10-21

10-20

t (ms)-5 -4 -3 -2 -1 0 1 2 3 4 5

I (µ

A)

-4

-3

-2

-1

0

1

2

3

4

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DRAIN CURRENT NOISE (3)

- Fundamental• thermal noise

- Excess noise• RTS• 1/f

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GATE CURRENT NOISE (4)

-VGS (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cur

rent

s (A

)

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

ID

IS

IG

IB

- Fundamental level• Shot noise

- Excess noise• RTS• 1/f

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Introduction (5)

- Drain current spectral density is dependent of :

• Technology process

• Oxide thickness

• Mobility

• Channel geometry (W, L)

•Access resistances

• Biases

Are commercial simulators well suited ?

- Gate current spectral density : few investigations up today

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Outline

• Introduction

• Methodology and Instrumentation

• 1/f modeling– 1/f theory– 1/f models

• Experimental results

• Conclusion

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

USED METHODOLOGY

Good model for F.E.T devices.

ic = source-drain noise generator transistor channel

ig = gate-source noise generator command electrode /channel

)f(S

)f(S

)f(S

cg

g

c

ii

i

i

Direct measurement of Coherence

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Simultaneous measurements

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EXPERIMENTAL SETUP

DrainGate

channel B channel A

IEEE Bus

AmplifiervoltageAmplifier

Transimpedance

Oscilloscope spectrum Analyser

Transistor

Batteries

Faraday cage

Batteries

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Transimpedance Amplifier

f (Hz)100 101 102 103 104 105

SI(

f) (

A2 /H

z)10-26

10-25

10-24

Ieq = 50nA

K = 107 V/A

f (Hz)100 101 102 103 104

SI(

f) (

A2 /H

z)

10-28

10-27

10-26

Ieq = 500 pA

K = 108 V/A

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Voltage Amplifier

f (Hz)101 102 103 104 105 106

SV(f

) (V

2 /Hz)

10-19

10-18

10-17

Req= 40

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Cross Spectrum Measurements

A

A

Analyser Input  A

Analyser Input  B

eA

eA

f (Hz)101 102 103 104 105 106

SV(f

) (V

2 /Hz)

10-21

10-20

10-19

10-18

10-17

Req= 3

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Low noise Amplifiers

Voltage Amplifier Transimpedance Amplifier

Bandwidth 0.5Hz-1MHz/200Hz-30MHz 1 Hz- 200 KHz

Gain 1000 108 ; 107 ; 106

Input Imped. 1 M - 15 pF/ 1 M - 50 pF 1 - 10 k

Noise equival. 40 / 35 500 pA ; 50 nA ; 2 A

Used forDirect measure of SI(f)

Under low impedance

Direct measure of SI(f)

Under strong impedance

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Drain noise measurements

V S (t)

i

R P

G

R C

eA(t)

iRp(t)

Ch(t)Rp

Amplide tension

AnalyseurFFT

D

S

G

C

C

VGS

VDS

(f)S(f)SRR

RR(f)SG(f)S

PRchAS ii

2

Pc

Pce

2V

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Drain noise measurements

(f)S (f)SK (f)SAchS ii

2V

K

VS(t)

ich(t) iA(t)RC

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Outline

• Introduction

• Methodology and Instrumentation

• 1/f modeling– 1/f theory– 1/f models

• Experimental results

• Conclusion

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

1/f noise theory

Noise source due to conductivity fluctuations : = q µ n

three models :

Hooge model (µ) SPICE

Mc Whorter model (N)

correlated model (N- µ) BSIM

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N model

2D2

ditoxeffeff

Ft4I I

CCC

1LW

1f1

kTEN

qfSD

f

1

VV

I

WLC

1EkTNqfS

2TGS

2D

2ox

Ft2

ID

D2

oxeff

Ft2

I ILC

1µ

f1EkTNq

fSD

Weak inversion

Strong inversion : i) linear regime

ii) saturation regime

f1

VL

WkTENqfS 2

DS32effFt

2ID

2TGS32eff

Ft2

I VVL

Wµ

f1EkTNq

21

fSD

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Typical NMOS results

HUNT nMOS - W/L=10/3.0

ID (A)

10-8 10-7 10-6 10-5 10-4

SI D

(A

2 /H

z)

10-24

10-23

10-22

10-21

10-20

10-19

ID vs SID mesuré

VDS= 25mV

f=1 Hz

VT

(2)

(2)

HUNT - nMOS - W/L=10/3.0

ID (A)10-8 10-7 10-6 10-5 10-4 10-3

SI D

(A

2 /H

z)

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

ID vs SID mesuréVDS= 1V

f=1 Hz

VT

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µ model

Dox3eff

effHeffI IC

L

Wf

kTµ2fSD

TGS

2D

ox

HI VV

IWLC

1f

qfSD

2/3D3

ox

effHI I

WLC

µ

f2qfS

D

Weak inversion

Strong inversion : i) linear regime

ii) saturation regime

2DSTGS3oxH

2effI V

f1

VVL

WCqfS

D

3TGS3oxH2

effI VVL

WC

fqµ

21

fSD

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Typical PMOS results

HUNT - pMOS - W/L=10/3.0

ID (A)10-10 10-9 10-8 10-7 10-6 10-5

SI D

(A

2 /H

z)

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

ID vs SID

VDS= - 25mV

f=1 Hz

VT

(2)

(2)

(1)

HUNT - p-MOS - W/L=10/3.0

ID (A)10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

SI D

(A

2 /H

z)

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

ID vs SID VDS= - 1V

f=1 Hz

VT(2)

(3/2)

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CORRELATED MODEL (N- µ)

Fluctuation of oxide Trapped carriers quantity

Fluctuation of carriers number and of their mobility

NN

µµ

II

D

D

fS

Ig

gI

Cµ1I

fSFB

DV

2

D

m

2

m

Doxeff2

D

i

fCLW

NkTqfS

2ox

T2

VFB

: Coulomb scattering coefficient

: the electron tunneling constant in the oxide

NT : oxide trap density

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CONTRIBUTION OF ACCESS RESISTANCESCONTRIBUTION OF ACCESS RESISTANCES

VDS

VD

VG

VGS

VS

VDSint

VGSint

RD

RS

VDS

VD

VG

VGS

VS

VDSint

VGSint

RD

RS

VDS

VD

VG

VGS

VS

VDSintVDSint

VGSintVGSint

RD

RS

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CONTRIBUTION OF ACCESS RESISTANCESCONTRIBUTION OF ACCESS RESISTANCES

2

chmacc

ichmint2ch

2m

2acc

ii

intint

SRintintintintch

D

g2g2

R1

)f(S gg2g2g 4

R)f(S

)f(S

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Access resistance noise

HUNT nMOS - W/L=10/3.0

ID (A)

10-8 10-7 10-6 10-5 10-4

SI D

(A

2 /H

z)

10-24

10-23

10-22

10-21

10-20

10-19

ID vs SID mesuré

VDS= 25mV

f=1 Hz

VT

(2)

(2)

HUNT - pMOS - W/L=10/3.0

ID (A)10-10 10-9 10-8 10-7 10-6 10-5

SI D

(A

2 /H

z)

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

ID vs SID

VDS= - 25mV

f=1 Hz

VT

(2)

(2)

(1)

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

SPICE Simulations

LW C f

g K )f(S

effeffoxAF

2mF

IDHSPICE

SPICE [1980] LC f

I K )f(S

2effox

EF

AFDF

ID

SPICE [1996] LW C f

I K )f(S

eff effoxEF

AFDF

ID

NLEV=0

NLEV=1

NLEV=2 and 3

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BSIM MODELBSIM MODEL

Weak inversion :

Strong inversion :

2*

L

2LL

2

2D

pin

NN

NNOICNNOIBNOIA

LWf

IkTL

TGSox0 VVCqN with DsatDTGSoxL V,VminVVCqN and

fSfS

fS fSfS

limwi

limwiID

Continuity between weakand strong inversion :

2

L20L0*

L

*0

2D

2eff

I NNNOIC21

NNNOIBNN

NNLnNOIA

CfL

IkTqµfS

oxD

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BSIM MODELBSIM MODEL

Teffs N q 2

NOIB

TN q

NOIA

NOIA 4NOIB

NOIC2

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

• Introduction

• Methodology and Instrumentation

• 1/f modeling– 1/f theory– 1/f models

• Experimental results

• Conclusion

Outline

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Typical Results

Transistor PMOS C025MM W/L=10/10Group E: PMOS Device

VGS(V)

-5-4-3-2-10

g m(A

/V)

0.0

2.0e-7

4.0e-7

6.0e-7

8.0e-7

1.0e-6

1.2e-6

1.4e-6

1.6e-6

1.8e-6

2.0e-6

I D(A

)

-4.0e-6

-3.0e-6

-2.0e-6

-1.0e-6

0.0

ExperimentalSimulation

L=10 µm

VDS=-50 mV

Paramètres de simulation:VT= -1.71 V

o = 99 cm2V-1s-1

= 0.108 V-1

Racc = 144

L= -1.62 10-8 m

LW C f

g K )f(S

effeffoxAF

2mF

ID

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PMOS Results TOX=1.5 nm

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NMOS Results TOX=1.5 nm

NMOS W=0.1, L=10, VD=-25mV

VGS-VT (V)

10-3 10-2 10-1 100

SI D

(1 H

z) (

A2 /H

z)

10-21

10-20

10-19

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NOIA = 2,2.1020 (V-1.m-3) NOIB = 8,7.106 (V-1.m-1)NOIC = 8,6.10-8 (V-1.m)

Ohmic RangePMOS TOX = 1.3 nmW=10µm, L=0.35µm MINOXG L6 L3 PMOS

W=10, L=0.35, VD=-25mV, Simulation de SID(1 Hz)=f(-ID)

ID (A)10-9 10-8 10-7 10-6 10-5 10-4

SI D

(1

Hz)

(A

2 /Hz)

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

ExperimentalComputed

V

T

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NOIA = 2,2.1020 (V-1.m-3) NOIB = 8,7.106 (V-1.m-1)NOIC = 0 (V-1.m)

Ohmic RangePMOS TOX = 1.3 nm W=10µm, L=0.35µm MINOXG L6 L3 PMOS

W=10, L=0.35, VD=-25mV, Simulation de SID(1 Hz)=f(-ID)

ID (A)10-9 10-8 10-7 10-6 10-5 10-4

SI D

(1

Hz)

(A

2 /Hz)

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

ExperimentalComputed

VT

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Saturation RangePMOS TOX = 1.3 nm W=10µm, L=0.35µm

NOIA = 2,2.1020 (V-1.m-3) NOIB = 8,7.106 (V-1.m-1)NOIC = 8,6.10-8 (V-1.m)

MINOXG M5 L3 PMOSW=10, L=0.35, VD=-1V, Simulation de SID

(1 Hz)=f(-ID)

ID (A)

10-8 10-7 10-6 10-5 10-4 10-3

SI D

(1

Hz)

(A

2 /Hz)

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

ExperimentalComputed

VT

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Saturation RangePMOS TOX = 1.3 nm W=10µm, L=0.35µm

NOIA = 2,2.1020 (V-1.m-3) NOIB = 8,7.106 (V-1.m-1)NOIC = 0 (V-1.m)

MINOXG M5 L3 PMOSW=10, L=0.35, VD=-1V, Simulation de SID

(1 Hz)=f(-ID)

ID (A)

10-8 10-7 10-6 10-5 10-4 10-3

SI D

(1

Hz)

(A

2 /Hz)

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

ExperimentalComputed

VT

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

NOIA = 1.1022 (V-1.m-3) NOIB = 2,6.106 (V-1.m-1)NOIC = 7.10-11 (V-1.m)

Ohmic RangePMOS TOX = 1.5 nmW=0.3µm, L=10µm

HUNT2 (PLI 1032 D16) G3, G4, B5 LAF PMOSW=0.3, L=10, VD=-25mV, Simulation de SID

(1 Hz)=f(-ID)

ID (A)10-11 10-10 10-9 10-8 10-7 10-6

SI D

(1 H

z) (

A2 /H

z)

10-28

10-27

10-26

10-25

10-24

10-23

10-22

10-21

ExperimentalComputed

VT

VG=1V

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NOIA = 1.1022 (V-1.m-3) NOIB = 2,6.106 (V-1.m-1)NOIC = 0 (V-1.m)

Ohmic RangePMOS TOX = 1.5 nmW=0.3µm, L=10µm

HUNT2 (PLI 1032 D16) G3, G4, B5 LAF PMOSW=0.3, L=10, VD=-25mV, Simulation de SID

(1 Hz)=f(-ID)

ID (A)10-11 10-10 10-9 10-8 10-7 10-6

SI D

(1 H

z) (

A2 /H

z)

10-28

10-27

10-26

10-25

10-24

10-23

10-22

10-21

ExperimentalComputed

VT

VG=1V

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Saturation Range

NOIA = 1.1022 (V-1.m-3) NOIB = 2,6.106 (V-1.m-1)NOIC = 7.10-11 (V-1.m)

Simulation de SIG(1 Hz)=f(IG) pour HUNT2 (PLI1032 D16) B5LAF PMOS

W=0.3, L=10, VD=-1V

ID (A)10-10 10-9 10-8 10-7 10-6 10-5

S I D(1

Hz)

(A

2 /Hz)

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

ExperimentalComputed

PMOS TOX = 1.5 nmW=0.3µm, L=10µm

VT

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Saturation Range

NOIA = 1.1022 (V-1.m-3) NOIB = 2,6.106 (V-1.m-1)NOIC = 0 (V-1.m)

PMOS TOX = 1.5 nmW=0.3µm, L=10µmSimulation de SIG

(1 Hz)=f(IG) pour HUNT2 (PLI1032 D16) B5LAF PMOS

W=0.3, L=10, VD=-1V

ID (A)10-10 10-9 10-8 10-7 10-6 10-5

S I D(1

Hz)

(A

2 /Hz)

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

ExperimentalComputed

VT

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

-VGS (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cur

rent

s (A

)

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

ID

IS

IG

IB

PMOS TOX = 1.5 nm

VDS = -25 mV

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SIG(1 Hz)=f(IG) pour HUNT2 (PLI1032 D16) E7 LAF PMOS

W=0.3, L=10, VD=-25mV

IG (A)10-10 10-9 10-8 10-7 10-6 10-5

SI G

(f=1

Hz)

(A

2 /H

z)

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

(1,9)

Gate current noise (PMOS TOX = 1.5 nm)

VDS = -25 mV

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HUNT2 (PLI1032 D16) D2 LAF PMOS W=0.3, L=10,Cohérence HPD21_01 à VD=-25mV, VG=-0.5V

f (Hz)100 101 102 103 104

Coh

eren

ce

0.0

0.2

0.4

0.6

0.8

1.0

HUNT2 (PLI1032 D16) D2 LAF PMOS W=0.3, L=10,Cohérence HPD21_05 à VD=-25mV, VG=-1.5V

f (Hz)100 101 102 103 104

Coh

eren

ce

0.0

0.2

0.4

0.6

0.8

1.0

SID(1 Hz)=f(-(VGS-VT)) pour HUNT2 (PLI1032 D16) G3 G4 LAF PMOS

W=0.3, L=10, VD=-25mV

-(VGS-VT) (V)10-2 10-1 100 101

SI D

(f=1

Hz)

(A2

/Hz)

10-25

10-24

10-23

10-22

10-21

(1)

Coherence measurements(PMOS TOX = 1.5 nm)

VDS = -25 mV

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Conclusion

SPICE and HSPICE models are not well suited for 1/f noise

BSIM3 is a good fitting model

Thinner and thinner gate oxide new noise sources

© Estoril – 19 September 2003Advanced Compact Modeling Workshop

Conclusion

extGSV

iGD DRi

Source

extDSV

RS

RD

Grille Drain

intGSintm vg

intDSVy1intGSV

y3

intchgiGS

SRi

intchi