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ÉCOLE POLYTECHNIOUEFÉDÉRALE 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]
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 2
PART I: Charge-based DC, AC and Noise Modelling
☞Introduction: EKV v2.6
☞Charge-based Static Model
☞Quasi-static Charge & Transcapacitances Model
☞NQS Model
☞Noise Model
☞Mobility Model & Short-Channel Effects
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 3
Introduction: EKV v2.6 MOS Transistor (MOST) Model
☞ Motivation:
✔RF circuit design requires complete MOST model from DC to RF, including noise.
✔All 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
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 4
Charge-based Static Model
☞ Bulk-reference, symmetric model structure.
☞ Drain current expression including drift and diffusion:
(1)
x
y
L
n+ n+p+
S
G
DB
VS
VG
VD
ID
p substrate
Leff
tox
ID VD
VS
VG
G
S
D
B
ID W µ Q′I–( )Vchd
xd-----------⋅ ⋅ ⋅=
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 5
Charge-based Static Model
☞ Integration of from source to drain:
(2)
Vch
VPVDVS
n VP⋅
Q′I–
C′ox-----------
ID
β-----
ID IF IR–=
gmd
β---------
gms
β---------
weak inversion
A
B
CD
E
strong inversion
Inve
rsio
n C
harg
e D
ensi
ty
Channel Voltage
β µ C′ox
Weff
Leff----------⋅ ⋅=
Q′I
ID βQ′I–
C′ox-----------
Vchd⋅VS
VD
∫β
Q′I–
C′ox-----------
Vchd⋅VS
∞
∫
IF VP VS–( )
βQ′I–
C′ox-----------
Vchd⋅∞
VD
∫
IR VP VD–( )
–= =
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 6
Drain Current Normalization and Pinch-off Voltage
☞ Current normalization using the Specific current :
(3)
☞ Pinch-off voltage accounts for...
✔threshold voltage and substrate effect
(4)
☞ Slope factor :
(5)
IS
ID IF IR– IS i f i r–( )⋅ 2nβUT2
i f i r–( )⋅= = =
VP
VTO γ 2qεsNsub( ) C′ox⁄=
VP VG VTO γ VG VTO Ψ0γ2---+
2+– Ψ0
γ2---+
–⋅––=
n
nVG∂
∂VP1–
1 γ2 Ψ0 VP+---------------------------+= =
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 7
Charge-based Static Model
☞ Normalized transconductance-to-current ratio vs. normal-
ized current 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!
1.0
0.8
0.6
0.4
0.2
0.0
g ms·
UT /
I D
0.001 0.01 0.1 1 10 100 1000
ID / IS
analytic interpolation measured characteristics for:
0.5 µm, GAMMA=0.64 √ V 0.7 µm, GAMMA=0.75 √ V 1 µm, GAMMA=0.72 √ V
2
4
68
0.1
2
4
68
1
2g m
s·U
T /
I D
0.001 0.01 0.1 1 10 100 1000
if = ID / IS
asymptotes analytical numerical
(GAMMA=0.7 √ V)
1/ √ if
gms UT⋅ ID⁄ID IS⁄
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 8
Drain Current and Pinch-off Voltage
☞ Valid from weak to strong inversion, and from linear to saturation.
☞ Accuracy of weak inversion slope and substrate effect.
✔no additional parameters used for adapting weak inversion slope
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
I D [
A]
3.02.52.01.51.00.50.0
VG [V]
VS=0V 0.5V 1V 1.5V
n-channelW=10 µmL=10 µmVD=3V
IS
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5543210
n-channelVTO=0.752 VGAMMA=0.755 ÃVPHI=0.576 VLETA=0.503WETA=0.256
simulated measured
W=20µmL=20µm
W=20µmL=0.7µm
W=0.8µmL=20µm
VG [V]
VS [V
]
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 9
Quasistatic Charge- & Transcapacitances Model
☞ Node charges: integration of inversion charge density along channel:
(6)
(7)
✔Drain and source charges are obtained using Ward’s charge partitioning scheme.
✔Single equation expressions are used from weak to strong inversion.
-1 0 1 2 3 4 5-0.3
0.6
-0.2
0.5
-0.1
0.4
0
0.3
0.1
0.2
QS & QD (VD=0V)
QS, QD (VD=2V)
QG (VD=2V)
QG (VD=0V)
VG [V]
QB
Charges normalized to WLCox [V]
COX C′ox W L⋅ ⋅=
QI W QI ′ x( ) xd⋅0
L
∫⋅= QD WxL--- QI ′ x( ) xd⋅ ⋅
0
L
∫⋅= QS QI QD–=
QB γ COX VP Ψ0+⋅ ⋅–n 1–
n------------ QI⋅
–= QG QI– QB Qox––=
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 10
(Trans-)Capacitances Model
☞ Transcapacitances: derivation with respect to the terminal voltage:
(8)
✔Accurate capacitances through all inversion levels.
✔Symmetric CGS and CGD at VD=VS=0.
1.0
0.8
0.6
0.4
0.2
0.0
Intr
insi
c C
apac
itan
ces
C/(
Co
xWL
)
3210
VG[V]
TOX=6.6nmVD=VS=0VW=200µm, L=5µm
Simulated:
Measured:CGB
CGG
CGD=CGS
0 1 2-0.1
0.8
0
0.7
0.1
0.6
0.2
0.5
0.3
0.4
CGS (VG=2V)
CGD (VG=2V)
CGB (VG=2V)
CGB (VG=0.8V)
CGS (VG=0.8V)
CGD (VG=0.8V)
CBD (VG=2V)
CBD (VG=0.8V)
VDB [V]
No
rmal
ized
intr
insi
c ca
pac
itan
ces
CMN VN∂∂± QM( )= M N, G D S B, , ,=
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 11
Intrinsic MOST - Small Signal Equivalent
✔First-order model for the transadmittances using bias-dependent time constant :
(9)
(10)
Cgs Cgd
Cgb
CbdCbs
G
D
B
Ym g ∆Vg
Ym s ∆Vs
Ym d ∆Vd
S Transcapacitances are not shown
Distributed time constant accountingfor “transmission line effect”
τ
Ym g d s, ,( ) v g d s, ,( )∂∂i d≡
gm g d s, ,( )1 s τ⋅+---------------------= with τ τ0 f i f i r,( )⋅=
τ0L
2
2 µ UT⋅ ⋅----------------------=
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 12
Non-Quasistatic Model
☞ Intrinsic MOST: effect of QS/NQS models on charges-trans-capacitances- 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.
Q (QS)
C (QS)
C (NQS)
Q (NQS)
mag(Y21) phase(Y21) C (QS)
Q (NQS)
Q (QS)
C (NQS)Q: chargeC: capacitance
Model:
W/L=36x9/2
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 13
Noise Model
☞ Thermal noise is proportional to total inversion charge .
✔Valid for all inversion levels, and from linear to saturation.
☞ 1/f noise modelling included.
3-Feb-99
13:54:29
File : noise.cou
ELDO v4.6_1.1 (production) : * M.BUCHER - LEG/DE/EPFL
5e-01 1e+061e+051e+01 1e+041e+02 1e+03
Hz
-165
-120
-160
-125
-155
-130
-150
-135
-145
-140
dB
DB(INOISE)_1:3 DB(INOISE)_2:3 DB(INOISE)_3:3 DB(INOISE)_4:3
DB(INOISE)_5:3
5e-01 1e+061e+051e+01 1e+041e+02 1e+03
Hz
-250
-190
-240
-200
-230
-210
-220
dB
DB(ONOISE)_1:3 DB(ONOISE)_2:3 DB(ONOISE)_3:3 DB(ONOISE)_4:3
DB(ONOISE)_5:3
input noise PSD
output noise PSD
-260
-250
-240
-230
-220
-210
Nois
e P
SD
[dB
v/ÃH
z]
1.21.00.80.60.40.20.0
VDS [V]
f = 1kHzKF = 0 (no 1/f noise)
EKV model
LEVEL 3
QI
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 14
Mobility Model
☞ Field- and position-dependent mobility:
(11)
☞ One parameter: vertical critical field in the oxide
✔ for n-channel, for p-channel)
✔No back-bias dependence needed due to inclusion of bulk charge.
14x10-6
12
10
8
6
4
2
0
I D
3.02.52.01.51.00.50.0
VGS
n-channelW=L=10µmVDS=0.05 V
Measured SimulatedVB=0
VB=-1.5V
4x10-6
3
2
1
0
I D
-3.0-2.5-2.0-1.5-1.0-0.50.0
VGS
p-channelW=L=10µmVDS=0.05 V
Measured SimulatedVB=0
VB=1.5V
EKV v2.6 for 0.5um CMOS(NMOS, PMOS)
µ x( )µ0'
1Eeff x( )
E0----------------+
--------------------------= where: Eeff x( )Q'B x( ) η Q'inv x( )⋅+
ε0εsi
--------------------------------------------------=
E0
η 1 2⁄= η 1 3⁄=
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 15
Short-channel Effects
☞ Includes short-channel effects (here: 0.5um CMOS)
✔Velocity saturation, Channel length modulation (CLM), 2D-charge sharing, RSCE
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
I D [A
]
3.02.52.01.51.00.50.0
VG [V]
VS=0V 0.5V 1V 1.5V
n-channelW=10 µmL=0.5 µmVD=3V
IS
3.5x10-3
3.0
2.5
2.0
1.5
1.0
0.5
0.0
I D [A
]
3.02.52.01.51.00.50.0
VD [V]
10-6
10-5
10-4
10-3
10-2
g ds
[A/V
]
1V
VG=3V
2.5V
2V
1.5V
n-channelW=10 µmL=0.5 µmVS=0 V
50
40
30
20
10
0
-10
-20
∆VT [m
V]
0.1 1 10
Ldrawn [µm]
Measure Simulation
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 16
Summary
☞ EKV v2.6 MOST model is a charge-based compact model
✔Continuous, physics-based and valid for all bias conditions.
✔Includes 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 ver-sions).
☞ EKV v2.6 on the web: <http://legwww.epfl.ch/ekv/>
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 17
PART II: RF Application of the EKV v2.6 MOST Model
☞Intrinsic MOST and Extrinsic Parasitic Elements
☞RF Test Structure
☞Simulation and Measurement Environment
☞DC Measurements and Simulations
☞RF Measurements and Simulations
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 18
Intrinsic MOST and Extrinsic Parasitic Elements
Rs
CgsoCgs Cgd
Cgb
Rd
gdC jd
CbdCbs
Cjsgs
S
G
D
B
Ymg ∆Vg
Ym s ∆Vs
Ymd ∆Vd
L
WA s A d
Lov Lov
Cjs(d) = As(d) * Cj + Ps(d) * Cjsw
in trins ic partin trins ic pa rt
Structure of the MOST Corresponding small-signal
G
S D
Cov = W * Lov * Cox
As, Ad - area
Ps, Pd - perimeter
CgdoCgbo
EKV model
Rg
Rb
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 19
Simulation and Measurement Environment
☞ Measurements:
✔HP8510 and HP 8719 Network Analyzers
✔HP4145 and HP4156 DC Parameter Analyzers
✔Cascade HF Probe Station
✔Ground-Signal-Ground (GSG) probes
☞ Test Devices:
✔RF MOS transistor matrix with 36 parallel devices in GSG pad frame
✔Geometry of single circular MOST: L = 0.5 um, W = 9.2um
✔OPEN pad frame for de-embedding thru Y parameters
☞ Parameter Extraction and Simulation:
✔IC-CAP 5
✔ELDO v4.6 with EKV v2.6 (LEVEL=44)
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 20
RF Test Structure
☞ The GSG pad frame and matrix of the RF MOSTs✔Minimized extrinsic drain capacitance using circular layout
courtesy A.-S. Porret
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 21
DC Measurements and Simulations
☞ Transfer current and conductance characteristics
✔VD = 50mV
ID vs. VG gm vs. VG
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 22
DC Measurements and Simulations
☞ Output current and conductance characteristics
ID vs. VD gds vs. VD
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 23
RF Measurements and Simulations
☞ Measured de-embedded and simulated S-parameters
✔Frequency sweep 45MHz - 20 GHz
✔DC bias ID=18mA @ VG = 1.5 V VD = 3.0V
S11, S22 S12, S21
S11
S21
S12S22
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 24
RF Measurements and Simulations
☞ Real and Imaginary parts of the forward admittance Y21
Re(Y21) Im(Y21)
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 25
RF Measurements and Simulations
☞ Real parts of the input and output admittances Y11 , Y22
Re(Y11) Re(Y22)
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 26
RF Measurements and Simulations
☞ Maximum power gain Gmax
Gmax
ÉCOLE POLYTECHNIOUEFÉDÉRALE DE LAUSANNE
© MB-WG 1999 EKV MOS Transistor Modelling & RF Application 27
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)