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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]


© 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



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



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-----------⋅ ⋅ ⋅=




☞ 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–( )

–= =



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+---------------------------+= =




☞ 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⁄



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

]



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––=



(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, , ,=



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⋅ ⋅----------------------=



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



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



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⁄=



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



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/>



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



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



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)



RF Test Structure

☞ The GSG pad frame and matrix of the RF MOSTs✔Minimized extrinsic drain capacitance using circular layout

courtesy A.-S. Porret



DC Measurements and Simulations

☞ Transfer current and conductance characteristics

✔VD = 50mV

ID vs. VG gm vs. VG



DC Measurements and Simulations

☞ Output current and conductance characteristics

ID vs. VD gds vs. VD



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




☞ Real and Imaginary parts of the forward admittance Y21

Re(Y21) Im(Y21)




☞ Real parts of the input and output admittances Y11 , Y22

Re(Y11) Re(Y22)




☞ Maximum power gain Gmax

Gmax



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)

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