1. No category

ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
HP-RF MOS Modelling Workshop, Munich, February 15-16, 1999
EKV MOS Transistor Modelling & RF Application
Matthias Bucher, Wladek Grabinski
Electronics Laboratory (LEG)
Swiss Federal Institute of Technology, Lausanne (EPFL)
☞Part
I: Charge-based DC, AC and Noise Modelling
☞Part II: RF Application
[email protected] [email protected]
PART I: Charge-based DC, AC and Noise Modelling
☞Introduction:
EKV v2.6
☞Charge-based
☞Quasi-static
☞NQS
Charge & Transcapacitances Model
Model
☞Noise
Model
☞Mobility
© MB-WG 1999
Static Model
Model & Short-Channel Effects
EKV MOS Transistor Modelling & RF Application
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Introduction: EKV v2.6 MOS Transistor (MOST) Model
☞
Motivation:
✔RF
✔All
☞
circuit design requires complete MOST model from DC to RF, including noise.
current levels need to be well modelled, in particular also moderate inversion.
EKV v2.6 in summary:
✔A
physics-based compact MOST model in the public domain.
✔Dedicated
to analog circuit simulation for submicron CMOS.
✔Includes
weak-moderate-strong inversion modelling, doping & mobility effects,
short-channel effects, geometry- and bias-dependent matching.
✔Small
number of intrinsic model parameters:
EKV v2.6: < 20, BSIM3v3: > 65, MM9: > 55
© MB-WG 1999
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EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
Charge-based Static Model
VD
B
VG
VS
D
D
ID
G
S
ID
L
VD
G
B
tox
p+
n+
Leff
y
n+
x
S
VG
VS
p substrate
☞
Bulk-reference, symmetric model structure.
☞
Drain current expression including drift and diffusion:
dV ch
I D = W ⋅ µ ⋅ ( – Q′ I ) ⋅ ----------dx
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
(1)
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Charge-based Static Model
Inversion Charge Density
– Q′ I
----------C′ ox
☞
n ⋅ VP
W eff
β = µ ⋅ C′ ox ⋅ ---------L eff
strong inversion
B
I D = IF – I R
g ms
--------β
ID
----β
E
g md
--------β
weak inversion
Channel Voltage
Vch
C
D
VD VP
A
VS
Integration of Q′ I from source to drain:
∞
∫
VS
© MB-WG 1999
β
∫
VS
VD
–
∫
β
∞
– Q′
 -----------I ⋅ dV
ch
 C′ ox
(2)









ID = β
– Q′
 -----------I ⋅ dV =
ch
 C′ ox
– Q′
 -----------I ⋅ dV
ch
 C′ ox 









VD
IF ( VP – V S )
IR ( VP – VD )
5
EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
Drain Current Normalization and Pinch-off Voltage
☞
Current normalization using the Specific current I S :
2
I D = I F – I R = I S ⋅ ( i f – i r ) = 2nβU T ⋅ ( i f – i r )
☞
Pinch-off voltage V P accounts for...
✔threshold
voltage
V TO and substrate effect γ = ( 2qε s N sub ) ⁄ C′ ox
V P = V G – V TO – γ ⋅
☞
(3)
γ 2 
γ

V G – V TO + Ψ 0 + --- – Ψ 0 + ---


2
2
(4)
Slope factor n :
∂V P
n =
∂ VG
© MB-WG 1999
–1
γ
= 1 + --------------------------2 Ψ0 + VP
EKV MOS Transistor Modelling & RF Application
(5)
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FÉDÉRALE DE LAUSANNE
Charge-based Static Model
2
analytic interpolation
1.0
1
1/ √if
4
2
0.1
8
6
asymptotes
analytical
numerical
(GAMMA=0.7 √V)
4
0.01
0.1
0.6
0.4
0.2
2
0.001
measured characteristics for:
0.5 µm, GAMMA=0.64 √V
0.7 µm, GAMMA=0.75 √V
1 µm, GAMMA=0.72 √V
0.8
gms·UT / ID
gms·UT / ID
8
6
1
10
100
0.0
0.001
1000
0.01
0.1
if = ID / IS
☞
1
10
100
1000
ID / I S
Normalized transconductance-to-current ratio g ms ⋅ U T ⁄ I D vs. normalized current I D ⁄ I S from weak through moderate to strong inversion.
✔Comparison
with numerical solution of the Poisson equation.
✔Comparison
with three different CMOS processes (long-channel devices in saturation).
✔Almost
technology independent!
© MB-WG 1999
7
EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
Drain Current and Pinch-off Voltage
-3
10
n-channel
W=10 µm
-5 L=10 µm
10 VD=3V
-4
10
4.0
IS
-7
10
-8
10
VS [V]
-6
10
ID [A]
W=20µm
L=0.7µm
3.5
3.0
2.5
2.0
W=0.8µm
L=20µm
1.5
1.0
-9
10
W=20µm
L=20µm
simulated
measured
n-channel
VTO=0.752 V
GAMMA=0.755 √V
PHI=0.576 V
LETA=0.503
WETA=0.256
0.5
10
-10
10
-11
10
-12
0.0
0.0
VS=0V
0.5
1V
0.5V
1.0
1.5
1.5V
2.0
2.5
-0.5
0
1
2
3.0
3
4
5
VG [V]
VG [V]
☞
Valid from weak to strong inversion, and from linear to saturation.
☞
Accuracy of weak inversion slope and substrate effect.
✔no
© MB-WG 1999
additional parameters used for adapting weak inversion slope
EKV MOS Transistor Modelling & RF Application
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FÉDÉRALE DE LAUSANNE
Charges normalized to WLCox [V]
Quasistatic Charge- & Transcapacitances Model
0.6
0.5
0.4
QG (VD=0V)
0.3
0.2
QG (VD=2V)
C OX = C′ ox ⋅ W ⋅ L
0.1
0
QS, QD (VD=2V)
-0.1
QB
QS & QD (VD=0V)
-0.2
-0.3
-1
0
1
2
3
4
5
VG [V]
☞
Node charges: integration of inversion charge density along channel:
L
L
x
Q D = W ⋅ ∫ --- ⋅ Q I ′ ( x ) ⋅ dx
L
Q I = W ⋅ ∫ Q I ′ ( x ) ⋅ dx
0
(6)
0
n–1
Q B = – γ ⋅ C OX ⋅ V P + Ψ 0 –  ------------ ⋅ Q I
n
✔Drain
QS = QI – QD
Q G = – Q I – Q B – Q ox
(7)
and source charges are obtained using Ward’s charge partitioning scheme.
✔Single
equation expressions are used from weak to strong inversion.
© MB-WG 1999
9
EKV MOS Transistor Modelling & RF Application
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(Trans-)Capacitances Model
0.8
TOX=6.6nm
VD=VS=0V
W=200µm, L=5µm
0.6
0.8
CGG
0.7
Normalized intrinsic capacitances
Intrinsic Capacitances C/(CoxWL)
1.0
CGD=CGS
0.4
Simulated:
0.2
CGS (VG=2V)
0.6
0.5
CGD (VG=2V)
0.4
CGS (VG=0.8V)
0.3
CGB (VG=0.8V)
0.2
CBD (VG=2V)
CGB (VG=2V)
0.1
Measured:
CGD (VG=0.8V)
CBD (VG=0.8V)
CGB
0
0.0
-0.1
0
1
2
0
3
1
2
VDB [V]
VG[V]
☞
Transcapacitances: derivation with respect to the terminal voltage:
C MN = ±
✔Accurate
M, N = G, D, S, B
(8)
capacitances through all inversion levels.
✔Symmetric
© MB-WG 1999
∂
(Q )
∂ VN M
CGS and CGD at VD=VS=0.
EKV MOS Transistor Modelling & RF Application
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Intrinsic MOST - Small Signal Equivalent
G
C gs
Ym g ∆V g
Cgd
C gb
Ym s ∆V s
S
Transcapacitances are not shown
D
Ym d ∆V d
Distributed time constant accounting
for “transmission line effect”
Cbd
C bs
B
✔First-order
model for the transadmittances using bias-dependent time constant
Y m ( g, d, s ) ≡
∂i d
g m ( g, d, s )
= -------------------1+s⋅τ
∂ v ( g, d, s )
τ:
with τ = τ 0 ⋅ f ( i f, i r )
(9)
2
L
τ 0 = ---------------------2 ⋅ µ ⋅ UT
© MB-WG 1999
(10)
11
EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
Non-Quasistatic Model
mag(Y21)
phase(Y21)
C (QS)
Q (QS)
C (QS)
Q (NQS)
Model:
Q: charge
C: capacitance
W/L=36x9/2
☞
C (NQS)
C (NQS)
Q (QS)
Q (NQS)
Intrinsic MOST: effect of QS/NQS models on charges-transcapacitances- and capacitances-only models.
✔Y21
Phase prediction is similar for all models except C-only QS model.
✔Y21
Magnitude prediction is incorrect for Q (QS) and C (QS) models.
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
Noise Model
3-Feb-99
File : noise.cou
13:54:29
ELDO v4.6_1.1 (production) : * M.BUCHER - LEG/DE/EPFL
DB(INOISE)_1:3
dB
DB(INOISE)_2:3
DB(INOISE)_3:3
DB(INOISE)_4:3
DB(INOISE)_5:3
-120
input noise PSD
-125
-130
-210
-135
f = 1kHz
KF = 0 (no 1/f noise)
Noise PSD [dBv/√Hz]
-140
-145
-150
-155
-160
-165
5e-01
1e+01
1e+02
1e+03
1e+04
1e+05
1e+06
Hz
DB(ONOISE)_1:3
dB
DB(ONOISE)_2:3
DB(ONOISE)_3:3
DB(ONOISE)_4:3
DB(ONOISE)_5:3
-190
output noise PSD
-200
-220
-230
EKV model
-240
-250
LEVEL 3
-210
-260
0.0
-220
0.2
-230
0.4
0.6
0.8
1.0
1.2
VDS [V]
-240
-250
5e-01
1e+01
1e+02
1e+03
1e+04
1e+05
1e+06
Hz
Thermal noise is proportional to total inversion charge Q I .
☞
✔Valid
for all inversion levels, and from linear to saturation.
1/f noise modelling included.
☞
© MB-WG 1999
13
EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
Mobility Model
-6
4x10
14x10
n-channel
W=L=10µm
VDS=0.05 V
12
10
-6
p-channel
W=L=10µm
VDS=0.05 V
3
EKV v2.6 for 0.5um CMOS
(NMOS, PMOS)
ID
ID
8
2
6
4
Measured
Simulated
VB=0
2
Measured
Simulated
1
VB=0
VB=1.5V
VB=-1.5V
0
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
-0.5
-2.0
-2.5
-3.0
Field- and position-dependent mobility:
µ 0'
µ ( x ) = -------------------------E eff ( x )
1 + ---------------E0
☞
-1.5
VGS
VGS
☞
-1.0
where:
Q' B ( x ) + η ⋅ Q' inv ( x )
E eff ( x ) = -------------------------------------------------ε 0 ε si
(11)
One parameter: E0 vertical critical field in the oxide
✔
η = 1 ⁄ 2 for n-channel, η = 1 ⁄ 3 for p-channel)
✔No
back-bias dependence needed due to inclusion of bulk charge.
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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Short-channel Effects
50
n-channel
3.0 W=10 µm
L=0.5 µm
2.5 VS=0 V
40
VG=3V
2.5V
2.0
2V
1.5
1.0
∆VT [mV]
ID [A]
3.5x10-3
20
10
0
Measure
Simulation
-10
1.5V
0.5
30
-20
0.1
1V
1
0.0
-2
10
-3
10
-4
10
-5
10
-2
10
-3
n-channel
W=10 µm
L=0.5 µm
10-4 VD=3V
ID [A]
gds [A/V]
10
10
-5
10
-6
10
-7
10
-8
10
-9
-10
10
10
-6
0.0
IS
VS=0V
1.5V
1V
0.5V
-11
10
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.5
1.0
VD [V]
☞
10
Ldrawn [µm]
1.5
2.0
2.5
3.0
VG [V]
Includes short-channel effects (here: 0.5um CMOS)
✔Velocity
saturation, Channel length modulation (CLM), 2D-charge sharing, RSCE
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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ÉCOLE POLYTECHNIOUE
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Summary
☞
EKV v2.6 MOST model is a charge-based compact model
✔Continuous,
✔Includes
physics-based and valid for all bias conditions.
charge-based static and dynamic models, and noise.
✔Non-quasistatic
☞
(NQS) model for small-signal.
Availability early ‘99:
✔Eldo,
SmartSpice, Saber, Spectre, HSpice, PSpice, Aplac, Smash (check model versions).
☞
EKV v2.6 on the web: <http://legwww.epfl.ch/ekv/>
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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ÉCOLE POLYTECHNIOUE
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PART II: RF Application of the EKV v2.6 MOST Model
☞Intrinsic
☞RF
MOST and Extrinsic Parasitic Elements
Test Structure
☞Simulation
and Measurement Environment
☞DC
Measurements and Simulations
☞RF
Measurements and Simulations
© MB-WG 1999
17
EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
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Intrinsic MOST and Extrinsic Parasitic Elements
Corresponding small-signal
EKV model
Structure of the MOST
G
Rg
intrinsic part
Lov
G
S
intrinsic part
Lov
C gs
D
Cgso
Y m g ∆Vg
C gd
C gbo C gdo
C gb
S
L
Y m s ∆Vs
Rs
Rd
D
Y m d ∆Vd
gs
As
W
Ad
Cjs
C jd
gd
C bd
C bs
B
Cjs(d) = As(d) * Cj + Ps(d) * Cjsw
Cov = W * Lov * Cox
Rb
Ps, Pd - perimeter
As, Ad - area
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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Simulation and Measurement Environment
☞
Measurements:
✔HP8510
and HP 8719 Network Analyzers
✔HP4145
and HP4156 DC Parameter Analyzers
✔Cascade
HF Probe Station
✔Ground-Signal-Ground
☞
Test Devices:
✔RF
MOS transistor matrix with 36 parallel devices in GSG pad frame
✔Geometry
✔OPEN
☞
(GSG) probes
of single circular MOST: L = 0.5 um, W = 9.2um
pad frame for de-embedding thru Y parameters
Parameter Extraction and Simulation:
✔IC-CAP
✔ELDO
5
v4.6 with EKV v2.6 (LEVEL=44)
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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ÉCOLE POLYTECHNIOUE
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RF Test Structure
courtesy A.-S. Porret
☞
The GSG pad frame and matrix of the RF MOSTs
✔Minimized
© MB-WG 1999
extrinsic drain capacitance using circular layout
EKV MOS Transistor Modelling & RF Application
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FÉDÉRALE DE LAUSANNE
DC Measurements and Simulations
ID vs. VG
☞
gm vs. VG
Transfer current and conductance characteristics
✔VD
= 50mV
© MB-WG 1999
21
EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
DC Measurements and Simulations
ID vs. VD
☞
gds vs. VD
Output current and conductance characteristics
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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RF Measurements and Simulations
S11, S22
S12, S21
S21
S22
S12
S11
☞
Measured de-embedded and simulated S-parameters
✔Frequency
✔DC
sweep 45MHz - 20 GHz
bias ID=18mA @ VG = 1.5 V VD = 3.0V
© MB-WG 1999
23
EKV MOS Transistor Modelling & RF Application
ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
RF Measurements and Simulations
Re(Y21)
☞
Im(Y21)
Real and Imaginary parts of the forward admittance Y21
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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ÉCOLE POLYTECHNIOUE
FÉDÉRALE DE LAUSANNE
RF Measurements and Simulations
Re(Y22)
Re(Y11)
☞
Real parts of the input and output admittances Y11 , Y22
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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ÉCOLE POLYTECHNIOUE
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RF Measurements and Simulations
Gmax
☞
Maximum power gain Gmax
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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ÉCOLE POLYTECHNIOUE
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Summary
☞
Application of the physics-based EKV v2.6 MOST model for RF
simulation has been presented
✔DC
parameter set was verified on the RF MOST test structure measurements
✔The
small-signal characteristics were corrected for interconnections and bond pads
parasitics
✔Effective
gate and bulk (substrate) resistances were introduced to allow proper small
signal simulation
✔Simulated
small-signal S- and Y- parameters match on-the-wafers measurements over
wide range of frequencies (45MHz - 20GHz)
© MB-WG 1999
EKV MOS Transistor Modelling & RF Application
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