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© 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
© 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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
DRAIN CURRENT NOISE (3)
- Fundamental• thermal noise
- Excess noise• RTS• 1/f
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
Simultaneous measurements
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
EXPERIMENTAL SETUP
DrainGate
channel B channel A
IEEE Bus
AmplifiervoltageAmplifier
Transimpedance
Oscilloscope spectrum Analyser
Transistor
Batteries
Faraday cage
Batteries
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
Drain noise measurements
(f)S (f)SK (f)SAchS ii
2V
K
VS(t)
ich(t) iA(t)RC
© 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
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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)
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
PMOS Results TOX=1.5 nm
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© 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 = 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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© 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 = 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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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
© Estoril – 19 September 2003Advanced Compact Modeling Workshop
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