mos-ak 2009 eee / ntu unification of mos compact models...

MOS-AK 2009 EEE / NTU

X. ZHOU 1 © 2009

Xing Zhou

School of Electrical and Electronic Engineering &Institute for Sustainable Nanoelectronics,

Nanyang Technological University, Singapore

December 9, 2009

Email: [email protected]

Unification of MOS Compact Models with the Unified Regional Modeling Approach

Unification of MOS Compact Models with the Unification of MOS Compact Models with the Unified Regional Modeling ApproachUnified Regional Modeling Approach

MOSMOS--AK Workshop AK Workshop –– Johns Hopkins University, Baltimore, USAJohns Hopkins University, Baltimore, USA


X. ZHOU 2 © 2009

Presentation OutlinePresentation Outline

Motivation for MOS Model Unification

Unified Regional Modeling (URM) Approach

Xsim Model Results and Ultimate Goals

Model extendibility and modeling effortsSeamless physical scalability

Key challenges: symmetry and body contact, doping scaling (non-charge-sheet), contact effect (SB/DSS)Unique features: decoupled regional surface-potential solution, bulk/ground-reference and source/drain by label, ambipolar SB model, and subcircuit model for DSS

Bulk-MOS current and charge modelsFB-SOI and s-DG FinFETsSiNW and SB/DSS MOSFETsXsim: history, evolution, and future goals


X. ZHOU 3 © 2009

Sah–Pao (input)Voltage Equation

Pao–Sah (output)Current Equation φs-based

Qi-based

Vt-basedQb linearization

Qi linearization

Iterative / explicit

1966 1978 1985 1995 2005

Po

isso

n +

GC

A

Classical bulk-CMOS

Non-classical CMOS

ChargeSheetModel(Qsc=Qb+Qi)

~40 yrs

SOISOI

MGMG

Bulk Voltage/Current Equations, CSM

New Voltage/Current Equations

Partially-Depleted (PD)Fully-Depleted (FD), Ultra-Thin Body (UTB)

Non-Charge-Sheet

Symmetric/Asymmetric Double Gate (s-DG/a-DG)

no

ntr

ivia

ln

on

triv

ial

extension

Tri-gate, GAA, Heterostructure (strained-Si), …

MOSFET Compact Models: History and FutureMOSFET Compact Models: History and Future

Body Contact/Floating Body


X. ZHOU 4 © 2009

Need for an Extendable Core Model for Future GenerationNeed for an Extendable Core Model for Future Generation

Vt-based models

Time

’60 ’70 ’80 ’90 ’00 ’10

Qi-based models

φs-based models

Pao–Sah

Bulk PD-SOI FD-UTB/SOI DG/GAA/SB/DSS

ID

Ids

DGS

B

History has witnessed generations of MOS models

(B)

Sub

ID

DGS

Sub

DGS DG1S

G2

IDID

and efforts required from one generation to the next …

— Need for a core model extendable to future generations,and with less duplicating efforts

Do we want XXX-SOI-PD/FD ?-Bulk

-DG/GAA

• BSIM-SOI/MG• PSP-SOI-PD/DD• HiSIM-SOI• ULTRA-SOI• Xsim


X. ZHOU 5 © 2009

Vg

Vs Vd

Vb

(a)

PD-SOI

toxf

tSi

εoxf

εoxb toxb

φs

φb

φ0

Vg

Vs Vd

Vb

(b)

FD-UTB/SOI

Vg

Vs Vd

Vb

(c)

a-DG

Vg

Vs Vd

Vg

(d)

s-DG

Vg

Vs Vd

(e)

'Bulk-UTB'

Vg

Vs Vd

Vb

(f)

Bulk

Vb = Vg

toxb = toxftSi

half s-DGtSi

toxb → ∞ φ'0 = 0

φ0 ≠ 0

φ'b ≈ 0

φb = 0

φb ≠ 0 φ'b ≠ 0

φ'0 = 0

φs = φb

PD-SOI FD-UTB/SOI a-DG s-DG UTB Bulk

φ'b = 0

φb = 0

Seamless Transformation and Unification of Seamless Transformation and Unification of MOSFETsMOSFETs


X. ZHOU 6 © 2009

Common/Independent Symmetric/AsymmetricCommon/Independent Symmetric/Asymmetric--DG MOSFETDG MOSFET

Common/symmetric-DG [FinFET]• Vg1 = Vg2 = Vg: two gates with one bias• Cox1 = Cox2: s-DG (Xo = TSi/2)• Full-depletion: VFD = Vg(Xd=TSi/2)• Cox1 ≠ Cox2: ca-DG (Xo < TSi)

Independent/asymmetric-DG [SOI]• Vg1 ≠ Vg2: ia-DG, biased independently• Zero-field location may be outside body• Consider two “independent” gates; linked

through full-depletion condition: Xd1 + Xd2 = TSi

Unification of MOS• SOI ← ia-DG ↔ ca-DG ↔ s-DG → bulk

Zero-field potential: φo [φo'(Xo) = 0]

Vg

Vs Vd

Toxφ0 L

TSi

Kox

Xo

φs

φs2

φo (φo' = 0)

(φo' = 0)Kox2 Tox2

(Xo)

x

(φo' = 0)

Vg2

φs2

(Vb)

Since Poisson equation cannot be integrated twice when doping is considered, we do not solve combined solutions at the two Si/SiO2 interfaces; instead, we solve the two separately with zero-field as the other ‘boundary’.

→

SiNW


X. ZHOU 7 © 2009

Our Approach: Unified Regional Model (URM)Our Approach: Unified Regional Model (URM)

Start with s-DG with doped body (two unknowns, φs and φo)

Extend URMURM approach to φs solution ⎯ finding the “full-depletion voltage” VFD

( )

' φεφε

−= − = +

≡ −

gf soxs s

Si ox

gf g FB

VE

T

V V V0oE =

1 2s s sφ φ φ= = ( )( )

0sgn , 2 ,

sgn , , ,

φ

ϕ

φ φ φ ϒ ϒ ε ε

ϕ ϕ ϕ γ γ ϒ ϕ φ

− = − = =

− = − ≡ ≡ ≡

gf s s o Si ox ox ox ox

gf s s o th th th

V f q C C T

v f v v v V v

p

( ) ( ) ( ) ( ) ( ) ( )2, , ϕϕ ϕϕϕ

ϕ ϕ ϕϕϕ ϕϕ − + −− − ⎡ ⎤= − + − + − − −⎣ ⎦s or r s ocrF

s os o cv v

srv

of v e e e e e e e

Scale with Nch, TSi, Tox, Kox in all regions ⎯ φs readily applicable in bulk Ids(φs) Bulk model for short-channel/higher-order effects can be easily extended

Extending to a-DG ⎯ two ‘independent’ s-DG coupled by one VFD(Vg1,Vg2)

Without solving coupled solutions, which is impossible (rigorously) for doped bodyRecoverable to s-DG, FD/PD-SOI, undoped, bulk ⎯ unification of MOS models

0

φ= Fp thv

iep n

Highly-doped body: Charge-sheet approximation (CSA), similar to bulk

Undoped/(lowly-doped) body: Non-CSA (2nd integral of Poisson)


X. ZHOU 8 © 2009

L

Xo

y

TSi + Tox2

n+n+

VS

VG2

VD

VB

Ψ(x, y)

φs1(y)

φs2(y)

φo(y)

NA − ND

Ei = −qφs(y)

DG

Bulk

PN

SB

VdVs Vd,sat

VG1

−Tox1

0

x

TSi

Generic DG/SOIGeneric DG/SOI--MOSFET With/Without Body ContactMOSFET With/Without Body Contact

Symmetry

Body Contact

Body dopingBody thickness

S/D Contact

Carrier type


X. ZHOU 9 © 2009

Regional Regional φφss Solutions and FullSolutions and Full--Depletion VoltageDepletion Voltage

( )2

22

A os o o Si

Si

qN XX Tφ φ

ε− = =

( ) ( )1, 1, 2, 2,d FD g FD d FD g FD SiX V X V T+ = ( ),, 2g FDD id F SX V T=

22

2 4 gbfsub Vϒ ϒφ

⎛ ⎞= − + +⎜ ⎟⎜ ⎟

⎝ ⎠

gfdv depVφ ϒ φ= +

FD condition: s-DG:

{ }, ;subd eff fdp de ϑ φφ φ δ=

{ }, ;dds seff rv t φφφφ ϑ δ=

{ }2gbfs htr tV v Wφ = − L

Symbols: MediciLines: Model (Xsim)

Common Gate Voltage, Vg (V)

-2 -1 0 1 2

Sur

face

Pot

entia

l, φ s (

V)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

φs

φacc

φs

φacc

φdep

φs

φacc

φdep

φvi

φs

φacc

φdep

φvi

φstr

φs

φacc

φdep

φvi

φstr

φdsφseff

φds

φstr

φvi

φdep

φacc

φs



-2 -1 0 1 2

Sur

face

Pot

entia

l, φ s (

V)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

VFB VFD Vt

φsφseffφdepφdv

φstr φacc

φds

a ceff dss cφ φ φ= + { }2gbra hcc tV v Wφ = + L

,

2

,

2 2

2 2 4 gf FA

SD

d D

id

Ff

XqNV

ϒφ ϒε

⎛ ⎞= = − + +⎜ ⎟⎜ ⎟

⎝ ⎠


X. ZHOU 10 © 2009

SurfaceSurface--Potential Derivatives and Regional ComponentsPotential Derivatives and Regional Components



-2 -1 0 1 2

dφs/d

Vg

(V/V

)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

φsφseffφdep

φdv

φacc

φstr

φds

Regional solutions scale with body doping (NA), body thickness (TSi), oxide thickness (Tox), and all terminal biases

Smooth higher-order derivatives

Regional charge model –key to physically-based parameter extraction

Foundation to unification of MOS compact models (bulk/SOI/DG/NW/SB/DSS)


X. ZHOU 11 © 2009

BodyBody--Doping Scaling: High to Zero (Doping Scaling: High to Zero (““UndopedUndoped””))

“Intrinsic”: NA – ND = ni (temp-dependent)Undoped = “pure” (ideal): NA = ND = 0

Nch = ni: not exactly symmetric

Nch = 0: exactly symmetric

Extrinsic: NA – ND > niHigh temperature

Vgb − VFB (V)-2 -1 0 1 2 3

d2 φ

s/dV

gb2

(V/V

2 )

-4

-2

0

2

4

Symbols: Newton−RaphsonLines: Model (Xsim)

Vgb − VFB (V)-2 -1 0 1 2 3

dφs/

dVgb

(V

/V)

0.0

0.5

1.0

(Vd = Vs = Vb = 0)

Nch (cm−3)

0

1010

1014

1017

1018

Seamless doping scaling

Key:has to be p0, not NA

10 exp sinh

2φ −⎡ ⎤⎛ ⎞−

= = ⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

F thv A Di i

i

N Nnp e n

n

2ϒ ε= Si oxoq p C


X. ZHOU 12 © 2009

Inversion Charge and Effective DrainInversion Charge and Effective Drain––Source Voltage Source Voltage

Gate−Bulk Voltage, Vgb (V)

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Effe

ctiv

e V

ds,e

ff C

ompo

nent

s (V

)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Effe

ctiv

e V

ds,e

ff C

ompo

nent

s (V

)

10-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-210-1100101

Vds,effVdb,effVsb,eff

Vds = 1.2 V, Vsb = 0 V


-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Nor

mal

ized

Inve

rsio

n C

harg

e, Q

i/Cox

(V

)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

qi =

Qi/C

ox =

γV

gt (

V)

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

RHS of Pao−SahLHS of Pao−Sah

( ) ( ) ( )φ ϒ φ= − − −i gb FB s sq y V V y y ( ) ( ) ( )( ) ( )2φ φϒ φ ϒ φ− −= + −s F cb thy V v

gt s th sV y y v e y( )

= =ii gt

ox

Q yq V

C

, , ,ds eff db eff sb effV V V= −

LHS RHS

Key to without requiring very accurate φs Key to symmetry without Vsb clipping


X. ZHOU 13 © 2009

UndopedUndoped--Body DG Body DG FinFETFinFET vs. GAA vs. GAA SiNWSiNW

FinFET (DG)

( )2

2c thV vi

Si

qnde

dxφφ

ε−= ( )1

c thV vi

Si

qnd dr e

r dr drφφ

ε−⎛ ⎞ =⎜ ⎟

⎝ ⎠

( ) ( )( )s c th o c thV v V vgf s i thV v e eφ φφ ϒ − −− = −

( ) ( ) 22

2gf c thV V vi

s c gf th

th

V y V v ev

ϒφ −⎧ ⎫⎪ ⎪⎡ ⎤ = − ⎨ ⎬⎣ ⎦⎪ ⎪⎩ ⎭L

( )( ) ( )

, sin4

s c c o c c

th th

V V V V

v vi ox Sigt c c i th th

Si th

C TV V v e v e

v

φ φϒϒ

ε

− −⎛ ⎞⎜ ⎟=⎜ ⎟⎝ ⎠

( ) ( )2 2, 2

φ φ+ −= s o c thV vigt c c

ox

RqnV V e

C

SiNW (GAA)

First integration

Second integration

Ignore the φo term

ε=ox o ox oxC K T ( )ln 1ε= +ox o ox oxC K R T R

Gate−Source Voltage, Vgs (V)

-0.5 0.0 0.5 1.0 1.5 2.0

No

rma

lize

d In

vers

ion

Ch

arg

e, V

gt (

V)

0.0

0.5

1.0

1.5

2.0

0.050.61.2

Vds (V)

Symbols: SiNWLines: FinFET


X. ZHOU 14 © 2009

Bulk/GroundBulk/Ground--Reference and Source/Drain by LabelReference and Source/Drain by Label

( )( ) ( )

,

,,

ds i b th ds eff

i b th i

s

s effb bd e b t

d

f hf

I q A v V

q A v q A v

I I

VV

β

β β

= + = −

= + − +(B)

Sub

Id

DGS

Ids

,, ,d effds ef sf effVVV = −

Is

S/D by label (layout)

Always Source Always Drain,, ,d effds ef b bf s effVVV = −

Effective drain–source voltage (Vds,eff)

S/D by convention (nMOS)

• Vd > Vs: Ids > 0 (D → S)• Vd < Vs: Ids < 0 (S → D)

• Vd > Vs: Ids > 0 (‘D’ → ‘S’)• Vd < Vs: Ids > 0 (‘D’ ↔ ‘S’)

FB: BC:

• By convention, nMOS Ids always flows from ‘D’ to ‘S’• Terminal swapping for –Vds: involving |Vds| in model

Key: Bulk/Ground-reference — auto switch to B/G-ref when body is biased or floatingIntrinsic Ids is an exact odd function of VdsPhysical modeling of asymmetric MOS (nontrivial with “terminal swapping” for negative Vds)


X. ZHOU 15 © 2009

GummelGummel Symmetry Test on Long/ShortSymmetry Test on Long/Short--Channel BulkChannel Bulk

Symbols: MediciLines: Model

Vx (V)

-1.0 -0.5 0.0 0.5 1.0

d2I d

s/dV

x2 (

μ S/V

μ m)

-40

-30

-20

-10

0

10

20

30

40

d2I d

s/dV

x2 (

mS

/Vμ m

)

-10

-5

0

5

10

tox = 2 nm

Nch = 6.8x10−17 cm−3

L = 10 μm

L = 90 nm

Vx

-0.15 0.00 0.15d

6 Id

s/d

Vx6

G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008.( )0 ,ds i b th ds effI q A v Vβ= +

0

0 ,1vo ds

dssd ds ds eff

g II

R I V=

+


X. ZHOU 16 © 2009

GummelGummel Symmetry Test on Symmetry Test on UndopedUndoped ss--DG Without BCDG Without BC

Symbol: MediciLine: Model

Vx (V)

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

d2 I ds/

dVx2

(mS

/V-μ

m)

-0.10

-0.05

0.00

0.05

0.10L = 10 μm, Tox = 3 nm, TSi = 20 nm

Vx (mV)-60 -40 -20 0 20 40 60

d6 I ds/

dVx6

-20

-10

0

10

20Vg

Vg

Vg − Vx Vg + Vx

“Floating body” (without body contact): Key – “ground-referenced” model

Vx step size: 10 mV

-1.5

0.0

1.5

0

5

10

Vx (V)-0.2 0.0 0.2

-50

0

50

Vx (V)-0.2 0.0 0.2

0.0

1.5

Ids I'ds

I''ds I'''ds

Identical curves with any Vg , , ,ds eff d eff s effV V V= − G. J. Zhu, et al., T-ED, 55(9), p. 2526, 2008.


X. ZHOU 17 © 2009

Modeling Asymmetric MOSFETModeling Asymmetric MOSFET

Symbols: MediciLines: Model

Drain−Source/Source−Drain Voltage, VDS or VSD (V)

0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt, |

I DS

| (m

A/μ

m )

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

VDS

VSD L = 90 nmtox = 2 nm

VDS or VSD (V)0.0 0.5 1.0 1.5 2.0

r out

(S

/μm

)

102

103

104

S D

G

B

G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008.

Xj,s = 80 nm, ND,s = 1019 cm−3; Xj,d = 30 nm, ND,d = 1018 cm−3

“Source” and “Drain” by label (rather than by MOS convention); i.e., VDS and VSD are different

Structural asymmetry (e.g., Xj, ND) can be captured by refitting physical parameters (e.g., vsat,s and vsat,d)

Models based on S/D terminal swapping for negative Vds at circuit level can never model asymmetric device easily (need to have two sets of symmetric model parameters)


X. ZHOU 18 © 2009

BulkBulk--Referenced Model: Transfer CharacteristicsReferenced Model: Transfer Characteristics


Gate−Bulk Voltage, Vgb (V)-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in−S

ourc

e C

urre

nt, I

ds (

A/μ

m)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

Vb = 0

-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in−S

ourc

e C

urre

nt, I

ds (

μA/ μ

m)

0

10

20

30

(Vds = 1.2 V)

Vs = 0.0, Vd = 1.2 V

Vs = 0.3, Vd = 1.5 VVs = 0.6, Vd = 1.8 V

L = 10 μm


-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Dra

in−S

ourc

e C

urre

nt,

I ds

(μA

/μm

)

0.0

0.5

1.0

1.5

2.0Vs = 0

Gate−Source Voltage, Vgs (V)-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Dra

in−S

ourc

e C

urre

nt,

I ds

(A/μ

m)

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

Vb = 0

Vb = −0.4 V

Vb = −0.8 V

Vb = −1.2 V

(Vds = 0.05 V)

L = 10 μm

Saturation Ids–Vgb Linear Ids–Vgs



X. ZHOU 19 © 2009

BulkBulk--Referenced Model: Output CharacteristicsReferenced Model: Output Characteristics

Long-Channel Ids–Vds L-Dependent Ids–Vds


Vg = 1.2 V

Vs = Vb = 0

Vds0.0 0.5 1.0

g ds

(mS

/μm

)

0

5

10


Drain−Source Voltage, Vds (V)0.0 0.5 1.0

Dra

in−S

ourc

e C

urre

nt,

I ds

(mA

/μm

)

-1.0

-0.5

0.0

0.5

1.0

L = 10 μmL = 1L = 0.5L = 0.25L = 0.18L = 0.09

(A single smoothing δs)


Drain−Source Voltage, Vds (V)-0.5 0.0 0.5 1.0

Dra

in−S

ourc

e C

urre

nt,

I ds

( μA

/ μm

)

-15

-10

-5

0

5

10

15

Vgs = 0.4 V

Vgs = 0.8 V

Vgs = 1.2 V

L = 10 μm

Vds (V)

0.0 0.5 1.0

r out (

Ω/μ

m)

103

104

105

106

107

108

(Vbs = 0)


X. ZHOU 20 © 2009

BulkBulk--Referenced Model: ShortReferenced Model: Short--Channel CharacteristicsChannel Characteristics

Linear Ids/gm–Vgs Output Ids/gds–Vds



-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Tra

nsco

nduc

tanc

e, g

m (

μS/μ

m)

0

50

100

150

200Vs = 0

Gate−Source Voltage, Vgs (V)-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Dra

in−S

ourc

e C

urre

nt, I

ds (

A/μ

m)

10-1810-1710-1610-1510-1410-1310-1210-1110-1010-910-810-710-610-510-410-3

Vb = 0

Vb = −0.4 V

Vb = −0.8 V

Vb = −1.2 V

(Vds = 0.05 V)

L = 90 nm

Vs = Vb = 0

Gate−Source Voltage, Vgs (V)0.0 0.2 0.4 0.6 0.8 1.0 1.2

Dra

in−S

ourc

e C

urre

nt, I

ds (

mA

/μm

)

0.0

0.2

0.4

0.6

0.8

1.0

Dra

in C

ondu

ctan

ce, g

ds (

mS

/μm

)

0

2

4

6

8

10

12


L = 90 nm Vg = 0.4 V Vg = 0.8 V

Vg = 1.2 V


X. ZHOU 21 © 2009

Regional Charge Model Variation: Regional Charge Model Variation: TToxox, , NNchch, and , and NNgategate

Symbol: MediciLines: Model (Xsim)


-2 -1 0 1 2

Gat

e C

apac

itanc

e, C

gg/W

L (μ

F/c

m2 )

0.0

0.5

1.0

1.5

2.0

2.5

(Vds = Vbs = 0)

Tox = 2 nm, Nch = 5x1017 cm−3

Tox = 1.5 nm

Tox = 2.0 nm

Tox = 2.5 nm

Nch = 1x1017 cm−3

Nch = 5x1017 cm−3

Nch = 1x1018 cm−3

Ngate = 1x1022 cm−3, κqm = 0



-2 -1 0 1 2G

ate

Cap

acita

nce,

Cgg

/WL

(μF

/cm

2 )

0.0

0.5

1.0

1.5

2.0

5x1019

5x1020

1x1022

(Vds = Vbs = 0)

Ngate (cm−3)

Ngate = 5x1020 cm−3

Tox = 2 nm, Nch = 5x1017 cm−3, κqm = 0

Using URM surface-potential solutions, physical effects can be separated in the regional charge model for meaningful and decoupled parameter extraction.

PAE PDE


X. ZHOU 22 © 2009

LongLong--Channel (Normalized) Channel (Normalized) TranscapacitancesTranscapacitances


-2 -1 0 1 2

Nor

mal

ized

Cap

acita

nce

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

d(C

gg/C

ox)/

dVgs

(1/

V)

-4

-2

0

2

4Symbols: MediciLines: Model (Xsim)

(Vds = 0.6 V, Vbs= 0)

CggCdgCsgCbg


X. ZHOU 23 © 2009

Gate Capacitance with Coupled PDE and QMEGate Capacitance with Coupled PDE and QME

Symbols: Medici Lines: Model (Xsim)


-2 -1 0 1 2

Gat

e C

apac

itanc

e, C

gg/W

L (μ

F/c

m2 )

0.0

0.5

1.0

1.5

Vbs = 0

−0.6 V

−1.2 V

Vds = 0

0.6 V

1.2 V

κqm = 1, Ngate = 5x1019cm−3


X. ZHOU 24 © 2009

ShortShort--Channel Channel CCgggg and and CCdgdg with Drainwith Drain--Bias VariationBias Variation


Gate−Bulk Voltage, Vgb (V)-2 -1 0 1 2

Nor

mal

ized

(C

gg,C

dg)/

Cox

(F

/F)

0.0

0.2

0.4

0.6

0.8

1.0

Leff = 90 nm

Tox = 2 nm

Nch = 5x1017 cm−3Cdg

Cgg

Vds = 0 V

Vds = 0.6 V

Vds = 1.2 V


X. ZHOU 25 © 2009

LengthLength--Dependent Dependent CCgggg with Bodywith Body--Bias Variation Bias Variation



-3 -2 -1 0 1 2

Nor

mal

ized

Cgg

/Cox

(F

/F)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Vbs = 0

Vbs = −0.6 V

L = 0.09, 0.25, 0.5 μm

Vbs = −1.2 V


X. ZHOU 26 © 2009

ShortShort--Channel Channel TranscapacitanceTranscapacitance Symmetry/Reciprocity Symmetry/Reciprocity

Drain−Source Voltage, Vds (V)-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Nor

mal

ized

Cap

acita

nces

(F

/F)

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Cgs

Cgd

Cdd

CbsCbd

Csd

Cds

CdgCsg

Css

CdbCsb

Leff = 90 nm

Tox = 2 nm

Nch = 5x1017 cm−3

Vgb = 1.2 V


-2 -1 0 1 2

Nor

mal

ized

Cap

acita

nces

(F

/F)

-0.2

0.0

0.2

0.4

0.6

Cbd, Cbs

Csd, Cds

Cdd, Css

Cgd, Cgs

Leff = 90 nm

Tox = 2 nm

Nch = 5x1017 cm−3

Vds = 0


X. ZHOU 27 © 2009

FBFB--SOI: LongSOI: Long--Channel CharacteristicsChannel Characteristics

Transfer Ids–Vgs Output Ids–Vds



-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt, l

og(I

ds)

(A/μ

m)

-17-16-15-14-13-12-11-10

-9-8-7-6-5-4-3

Dra

in C

urre

nt, I

ds (

mA

/ μm

)-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.050.61.2

Vds (V)

L = 1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3

“Floating-body” SOI model comparison with Medici device.


Drain−Source Voltage, Vds (V)

-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt, I

ds (

mA

/μm

)

-0.05

0.00

0.050.30.60.91.2

Vgs (V)

L = 1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3


X. ZHOU 28 © 2009

FBFB--SOI: ShortSOI: Short--Channel CharacteristicsChannel Characteristics




-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt, l

og(I

ds)

(A/μ

m)

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

Dra

in C

urre

nt, I

ds (

mA

/ μm

)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.050.61.2

Vds (V)

L = 0.1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3



-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt, I

ds (

mA

/μm

)

-1.0

-0.5

0.0

0.5

1.0

1.5

0.30.60.91.2

Vgs (V)

L = 0.1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3

“Floating-body” SOI model comparison with Medici device.


X. ZHOU 29 © 2009

ss--DG: Evaluation in SurfaceDG: Evaluation in Surface--PotentialPotential--Based Based IIdsds((φφss) Model) Model


Common Gate Voltage, Vg (V)-0.5 0.0 0.5 1.0 1.5

Dra

in C

urre

nt, I

ds (

mA

/μm

)

0.0

0.2

0.4

0.6

0.8

1.0

Dra

in c

urre

nt,

log(

I ds)

(A

/μm

)-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2

Ids

log(Ids)NA = 1018 cm−3

TSi = 50 nm

Tox = 3 nm

L = 1 μm

Vds = 0.05 VVds = 1.2 V


Common Gate Voltage, Vg (V)-0.5 0.0 0.5 1.0 1.5

Tra

nsco

nduc

tanc

e, g

ms

(mS

/μm

)

0

20

40

60

80

Tra

nsco

nduc

tanc

e, lo

g(g m

) (S

/μm

)

-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2

g m0

(μS

/μm

)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

gms

gm0

log(gm)

NA = 1018 cm−3

TSi = 50 nm

Tox = 3 nm

L = 1 μm

Vds = 0.05 VVds = 1.2 V

Linear/Saturation Current Transconductance

Doped symmetric-DG model (with depletion/volume-inversion) comparison with Medici device.


X. ZHOU 30 © 2009

ss--DG/FinFETDG/FinFET: Short: Short--Channel Transfer CharacteristicsChannel Transfer Characteristics

Transfer Ids–Vgs Transfer gm–Vgs

Symbols: MeasurementLines: Model (Xsim)s-DG FinFET


-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt,

I ds

(A/μ

m)

10-9

10-8

10-7

10-6

10-5

10-4

10-3

Dra

in C

urre

nt, I

ds (

mA

/ μm

)

0.00

0.05

0.10

0.15

0.20

0.25

0.050.61.2

L = 0.5 μm, TSi = 140 nm, Tox = 4 nm

Vds (V)



-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Tra

nsco

nduc

tanc

e, g

m (

S/μ

m)

10-9

10-8

10-7

10-6

10-5

10-4

Tra

nsco

nduc

tanc

e, g

m (

mS

/ μm

)

0.00

0.05

0.10

0.15

0.050.61.2

L = 0.5 μm, TSi = 140 nm, Tox = 4 nm

Vds (V)

Symmetric-DG FinFET model comparison with Measurement.


X. ZHOU 31 © 2009

ss--DG/FinFETDG/FinFET: Short: Short--Channel Output CharacteristicsChannel Output Characteristics

Output Ids–Vds Output gds–Vds



-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt,

I ds

(mA

/μm

)

-0.10

-0.05

0.00

0.05

0.10

0.15

Vgs (V)

L = 0.5 μm, TSi = 140 nm, Tox = 4 nm

0.00.30.6

1.20.9



-0.5 0.0 0.5 1.0 1.5 2.0D

rain

Con

duct

ance

, g d

s (S

/μm

)

10-5

10-4

10-3

Vgs (V)

L = 0.5 μm, TSi = 140 nm, Tox = 4 nm

0.00.30.6

1.2

0.9

Symmetric-DG FinFET model comparison with Measurement.


X. ZHOU 32 © 2009

SiNWSiNW: Model Scalability with Radius and Gate Length: Model Scalability with Radius and Gate Length

Radius Variation Gate Length Variation

Si-nanowire model comparison with Medici device.



-0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt,

I ds

(μA

)

0.05

0.10

0.15

0.20

Dra

in C

urre

nt,

log(

I ds)

(A

)

-15

-14

-13

-12

-11

-10

-9

-8

-7

-6

4681012

Lg = 5 μm, Tox = 2 nm

R (nm)

Vds = 0.05 V



-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Dra

in C

urre

nt,

I ds

(A)

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

R = 10 nmTox = 2 nm

Vds = 1.2 V

Lg (nm)

2030456590130

180250500100020005000


X. ZHOU 33 © 2009

SiNWSiNW: Model Applied to Measured : Model Applied to Measured SiNWSiNW


Si-nanowire model comparison with Measurement.

Symbols: MeasurementLines: Model (Xsim)


-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

I ds

(A)

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

0.051.2

Vds (V)

L = 180 nm, R = 2 nm, Tox = 4 nm Symbols: MeasurementLines: Model (Xsim)


-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

I ds

(μA

)

-10

-5

0

5

10 L = 180 nm, R = 2 nm, Tox = 4 nm

Vgs (V)

00.3

0.6

1.20.9


X. ZHOU 34 © 2009


1st-order Transfer gm–Vgs 1st-order Output gds–Vds




-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

gm

(μS

)

0

2

4

6

8

10

12

0.051.2

Vds (V)



-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

g ds

(S)

10-8

10-7

10-6

10-5

10-4

L = 180 nm, R = 2 nm, Tox = 4 nm

Vgs (V)

00.30.6

1.20.9


X. ZHOU 35 © 2009


2nd-order Transfer gm’–Vgs 2nd-order Output gds’–Vds




-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

gm

' (μS

/V)

0

5

10

15

20

25

30

0.051.2

Vds (V)



-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2g d

s' (

μS/V

)

-30

-20

-10

0

10

20L = 180 nm, R = 2 nm, Tox = 4 nm

Vgs (V)

00.30.6

1.20.9


X. ZHOU 36 © 2009

GAA GAA SiNWSiNW: : GummelGummel Symmetry Test (Measurement)Symmetry Test (Measurement)


I ds

(μA

)

-8

-6

-4

-2

0

2

4

6

8

0.40.60.81.01.2

L = 180 nm, R = 2 nm, Tox = 4 nm

Vg (V)

Vg

Vg/2 − Vx Vg/2 + Vx(ΔVx = 0.02 V)

dIds

/dV

x (μ

A/V

)

5

10

15

20

25

Vx (V)

-0.4 -0.2 0.0 0.2 0.4

d2I d

s/dV

x2 (μ A

/V2 )

-60

-40

-20

0

20

40

60

Vx (V)

-0.4 -0.2 0.0 0.2 0.4

d3 I ds/

dVx3 (

μ A/V

3 )

-0.6

-0.4

-0.2

0.0

0.2

0.4

(a) (b)

(d)(c)


X. ZHOU 37 © 2009

SchottkySchottky--Barrier MOSFET: Barrier MOSFET: AmbipolarAmbipolar CurrentCurrent



-2 -1 0 1 2

Dra

in C

urre

nt, I

ds (

A/μ

m)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

0.050.61.2

Vds (V)

ΦM,s/d = 4.6 eV

L = 65 nm, TSi = 20 nm, Tox = 3 nm

Hole tunneling Electron tunnelingElectron thermionicNo drift-diffusion!

VdVs

Vg

Vg

0L

TSi

x

y

Body Gate Oxide

Schottky Contact

S D

Tox

Gaussian box

Medici: two-carrierXsim: sum of two unipolar (Ids,n + Ids,p)

Ambipolar possible in undopedSB-MOS with mid-gap ΦM,s/d


X. ZHOU 38 © 2009

SBSB--MOS: Total Current = (Electron + Hole) CurrentsMOS: Total Current = (Electron + Hole) Currents



0.0 0.5 1.0 1.5 2.0 2.5 3.0

Dra

in C

urre

nt, I

ds (

A/μ

m)

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

00.30.60.91.2

Vgs (V)

L = 65 nm, TSi = 20 nm, Tox = 3 nm

ΦM,s/d = 4.6 eV

n + p

n

p

Ambipolar(In + Ip)current


X. ZHOU 39 © 2009

SBSB--MOS: Model Applied to Measured SBMOS: Model Applied to Measured SB--MOSMOS



-4 -2 0 2 4

log(

I ds)

(A

/ μm

)

-15-14-13-12-11-10

-9-8-7-6-5-4-3

0.050.30.61.22.5

L = 200 nm, R = 12.5 nm, Tox = 28 nm

Vds (V)

(a)ΦM,s = 4.73 eV

ΦM,d = 4.77 eVSymbols: MeasurementLines: Model (Xsim)


-4 -2 0 2 4

log(

I ds)

(A

/ μm

)

-15-14-13-12-11-10

-9-8-7-6-5-4-3

-0.05-0.3-0.6-1.2-2.5

Vds (V)

(b)

L = 200 nm, R = 12.5 nm, Tox = 28 nm

ΦM,s = 4.73 eV

ΦM,d = 4.77 eV

nMOS operation (+Vds) pMOS operation (−Vds)

SB-MOS model comparison with Measurement.(Same model and same device with different bias)

G. J. Zhu, et al., T-ED, 56(5), p. 1100, May 2009.


X. ZHOU 40 © 2009

DSSDSS--SiNWSiNW: : SubcircuitSubcircuit ModelModel

DSS-SiNW MOS subcircuit model comparison with Measurement.

G. J. Zhu, et al., SSDM, p. 402, Oct. 2009.

Symbols: TCAD (Medici)Lines: Model (Xsim)


0.0 0.5 1.0 1.5 2.0

Dra

in C

urr

ent,

I ds

(μA

)

0

10

20

30

40

0.5 1.0 1.5 2.0

g ds

Symbols: MesurementLines: Model (Xsim)

Gate−Source Voltage, −Vgs (V)

-0.5 0.0 0.5 1.0 1.5 2.0 2.5

Dra

in C

urre

nt, I

ds (

A)

-16-15-14-13-12-11-10-9-8-7-6-5-4-3

L = 100 nm, R = 10 nm Tox = 2nm

Vs VdVs'Leff

VgSB MOS

DSS MOS

S DVs Vd

Vg

Vg

y0

2R

Tox

r

0R

Lseg Lg

Dopant-Segregated Schottky (DSS) SiNW:

• Thermionic/tunneling (TT) + drift-diffusion (DD)• The unique convex curvature in Ids–Vds can

only be modeled by a subcircuit model:SBD (TT) + MOS (DD)


X. ZHOU 41 © 2009

XsimXsim: Basic Model Parameters: Basic Model Parameters

Physical parameters [6]• Oxide thickness (Tox), S/D junction depth (Xj)• Doping: channel (Nch), gate (Ngate), S/D (Nsd), overlap (Nov)

AC/Poly/QM parameters [8]• Bulk charge sharing (BCS): channel (λc), gate (λp), overlap (λov)• Potential barrier lowering (PBL): accumulation (αacc), depletion/inversion (αds)• Extrinsic: lateral spread (σ), inversion/bulk charge factor (νi, νb)

DC parameters [19]• Mobility: vertical-field mobility (μ, μ2, μ3, ν)• Effective field: vertical (ζn, ζb), lateral (δL)• PBL: accumulation (αacc), depletion/inversion (αds), long-channel DIBL (αdibl)• BCL/lateral-doping: BCL (λ), halo-peak (κ), halo-spread (β), halo-centroid (lμ)• Series resistance: bias-dependent (υ), bias-independent (ρ)• Velocity saturation (vsat), velocity overshoot (ξ), effective D/S voltage (δs)

Smoothing parameters — internal model requirement

Total: 33 basic parameters DG/SiNWhas less parameters


X. ZHOU 42 © 2009

XsimXsim: History, Evolution, and Philosophy: History, Evolution, and Philosophy

20071997 2000 20021998 1999 2001 20052003 2004 2006 2008

K.Y.Lim

URM URM VVtt--based bulkbased bulkS.B.Chiah

Karthik

G.H.See

URM URM VVtt--based bulk with nonbased bulk with non--pinned pinned φφss

URM URM VVtt//φφss--based strainbased strain--Si/DGSi/DG

URMURM φφss--based bulk/DGbased bulk/DG

Nonuniform/halo doping, vertical/lateral-field mobility, bias-dep Rsd, DIBL, CLM/VS/VO

Idrift+Idiff, URM Qb/Qi, 2D-BCS/PBL, PDE/PAE/PIE, QME, W-dep

SiGe(x)/doping-dep φs, TSi/doping-dep s/a-DG

SC-Q, B/G-ref, S/D by labelKey

mo

del

ed e

ffec

tP

hil

oso

ph

y • URM: Unified Regional Modeling approach — single-piece physics-based regional solutions• New model/effect includes old ones as special cases — extendibility and backward compatibility• One/two-iteration parameter extraction — minimum data requirement and predictability• Selectable accuracy within one parameter set — consistent full/simple model for design/verification


X. ZHOU 43 © 2009

XsimXsim: Future and Ultimate Goal: Future and Ultimate Goal

20061997 2010 20122009 2011 20152013 2014 20162007 2008

S.H.Lin GAA/GAA/SiNWSiNW/Mismatch/Statistical/Mismatch/StatisticalC.Q.Wei SelfSelf--heating/heating/SiNWSiNW--NoiseNoise

G.J.Zhu SB/DSS/UTBSB/DSS/UTB--SOI/DG/SOI/DG/SiNWSiNWJ.B.Zhang SOI/DG/LDMOSSOI/DG/LDMOS

Vt-b

ased

bu

lk

Str

ain

ed-S

i

φ s-b

ased

bu

lk

iaia--DG DG – most difficult, yet complete, structure containing the rest

ss--DG DG – key to extending to other device structures/operations

Ultimate Goal Ultimate Goal —— Unification of MOS models, with seamless transitions across device types/operations

Why not Xsim-SOI/DG/NW?They’re all physically related and should be modeled in one core rather than one for each.

caca--DG DG – bridging (common-gate) s-DG and (independent-gate) a-DG

SOI SOI – PD/FD, Nch/TSi scaling, with/without body contact

M.K.Srikanth Variability/ReliabilityVariability/Reliability


X. ZHOU 44 © 2009

Current team members (PhD students)• Shihuan Lin• Chengqing Wei• Guojun Zhu• Junbin Zhang• Machavolu Srikanth

Previous team members (PhD/MEng students)• Dr Khee Yong Lim• Yuwen Wang• Dr Siau Ben Chiah

Sponsorships and collaborators• Semiconductor Research Corporation• Chartered Semiconductor Manufacturing

AcknowledgmentAcknowledgment

• Dr Zuhui Chen• Ramachandran Selvakumar• Yafei Yan• William Chandra

• Dr Karthik Chandrasekaran• Dr Guan Huei See• Guan Hui Lim

Our relevant publications: http://www.ntu.edu.sg/home/exzhou/Research/DOUST/pub.htm

• Institute for Sustainable Nanoelectronics (ISNE)

• Atomistix Asia Pacific Pte Ltd• Institute of Microelectronics

Research Staff:

mos-ak 2009 eee / ntu unification of mos compact models...

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