drain current in silicon-based bulk and utbb- fdsoi ... · the channel only: quantum resistance 7 2...

Drain current in Silicon-based Bulk and UTBB-FDSOI devices: what are the key ingredients?

D. Rideau1, F. Monsieur1, O. Nier1,2, Y. M. Niquet3, V. Quenette1, G. Mugny1,5, G. Gouget1, M. Quoirin1, and R. Gonella1

1) STMicroelectronics, 850, rue J. Monnet, BP. 16, 38921 Crolles, France; 2) IMEP-LAHC, MINATEC 3 Parvis Louis Néel, 38016 Grenoble; 3) SP2M, UMR-E CEA/UJF-Grenoble 1, INAC, Grenoble, France

Outlook

• What drives the Linear current in ultra-short MOSFETs?

• NEGF vs Semi classical TCAD • A focus on the Near-LDD region •  the link bw Access Resistance and the ‘Apparent’ Channel

Mobility degradation.

• Investigation of the saturation regime • More NEGF simulations • Diffusive Model or Virtual Source Model? • Back to measurements

2

What drives the current reduction in Short Devices? 3

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.610-10

10-9

10-8

10-7

10-6

10-5

10-4

NORM

ALIZ

ED C

URRE

NT (A

)

GATE VOLTAGE (V)

Long device

Short device

•  Mobility Degradation •  Velocity Saturation •  Injection Velocity •  Pinch Off

è Focus on Silicon-based Field effect transistors curently in production (2016)

High VDS

Low VDS

•  Quantum Transport vs Classical one?

Focus on: è  Linear Channel Resistance

What drives the Linear current in ultra-short MOSFETs? 4 Long Channel Length

Short Channel Length (L~20nm)

Total Device Resistance is dominated by the ‘Long channel’ Channel mobility

The access Resistances reduce the current

Investigated: •  Do we have additional

mechanisms in the channel? Focus on: è Planar MOSFETs with

homogeneous channel (e.g. no pocket)

Total Device Resistance in the linear regime:

As e.g. [M. Zilli, et al., Electron Device Lett. 28, 1036 (2007).]

IVR D

ON =

Channel Resistance 2: L.(µ0

.COX )-1.(VG-VTH)-1 Access Resistance

Undoped Channel

SOI BOX

Spacer

2

HDD

1

1: R1

L

10 )( RrLRon +⋅= µ?

What drives the current in ultra-short MOSFETs? 5

DDTHGOX VVVVCLI )2/(0 −−⋅⋅=⋅ µDDTHG

DTHGOX

OX VVVVVVV

LCR

CLI )2/())2/()2(1( 00

0 −−−−⋅

⋅⋅⋅+

⋅=⋅

µµ

R0

Impact of R0 only? … or

Measured @ VD=50mV

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16x 10-6

NORM

ALIZ

ED C

URRE

NT (A

): I*L

/W

GATE VOLTAGE (V)

LCH=0.9 µmLCH=1.8 µm

LCH=0.45 µm

LCH=0.15 µm

LCH=50 nm

LCH=20 nm

µ0(L) due to additional mecanisms?

Access resistance:

Channel Mobility: L-dependent Mobility degradation

Linear Channel Current:

Capacitance

Outlook





6

The Channel Only: Quantum Resistance 7

2 4 6 8 10 12

x 1012

0

50

100

150

200

250

QUA

NTUM

RES

ISTA

NCE

[ Ω . µ

m]

INVERSION CHARGE [/cm2]

NEGF: (2nm<TSi<10nm)

Eq. 1

Quantum resistance calculated with NEGF for various channel thicknesses.

Resistance calculated with NEGF in an ideal channel-device.

Calculations TB_SIM

))(/(kTm2 THGQ VVCoxqR −⋅⋅⋅⋅≈ π

è NMOS: σΒ = 8.4 Ω.mm.V.

è 1)2( −⋅⋅= OXBB Cσµ of 23.8 cm2/(V.s.nm)

Mobility

{ }BTHGTHGOX

on VVVVCLR σ

µ⋅⋅

−+

⎭⎬⎫

⎩⎨⎧

−⋅= 2

)(1

)(1

0

Mobility with NEGF in O. Nier, et al., Journal of Computational Electronics 12.4, 675 (2013).

8 Simulation setups

http://www.synopsys.com/Tools/TCAD/ http://inac.cea.fr/L_Sim/TB_Sim

TB_SIM: -  self consistent NEGF -  Local + remote coulomb -  Band structure effects

Local Coulomb Remote Coulomb

PH + SR

Realistic Doping Profile from Process simulation

SYNOPSYS SDEVICE: -  Hydrodynamics with effective mobility -  Density gradient quantum correction

Varying channel length

Focus on: è Planar MOSFETs with

homogeneous channel (e.g. no pocket)

Access Region: NEGF vs Semi classical 9

0 0.05 0.1 0.15 0.2 0.2550

100

150

200

250

300

Ron Ω

. µ

m

L (µ m.)

VD 0.05V: Mean Error = 2.5e-014 %VD 0.05V: Mean Error = 0.17 %VD 0.05V: Mean Error = 0.22 %

All scatterings (EMA): µ0 =0.04

PHONON Only: µ0 =0.053

VD 0.05V: σ = 31 µ0 =0.028 Cox =0.025

VD 0.05V: σ = 31 µ0 =0.028 Cox =0.025

VD 0.05V: σ = 31 µ0 =0.028 Cox =0.025

All scatterings (kp2): µ0=0.028

VGT=0.8V

Ron = 126 (Ω.µm) = 46 + 40 * 2 (Ω.µm)

{ } 00

2)(2)(

1)(

1 RVVVVC

LR BLDDTHGTHGOX

on ⋅++⋅⋅−

+⎭⎬⎫

⎩⎨⎧

−⋅= σσµ

The Channel represent only 1/3 of the total Resistance in a 30 nm Device:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

50

100

150

200

250

300

350

400

450

500

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m] TCAD: σ = 33

R0 =18

NEGF(kp2): σ = 31 R0=1.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

500

1000

1500

Ron Ω

. µ

m

L (µ m.)

VD 0.005V: Mean Error = 0.45 %

TCAD: µ 0 = 0.025

NEGF(kp2): µ 0 = 0.028

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

50

100

150

200

250

300

350

400

450

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m] All scatterings (kp2): σ = 31

Phonon Only: σ = 11

All scatterings (EMA):: σ = 25

Quantum (RQ/2): σ = 8.4

10 )(22 −−⋅⋅+⋅= THG VVRR σ

Access Region: Quasi-Fermi Level 10

How can we bridge Quantum transport to semi-classical transport?

Method 1: Current comparison Method 2: Fermi level calculation assuming Fermi Dirac Distribution è Localize the most resistive regions.

NEGF: extraction of quasi Fermi level • Occupied local density-of-states map in energy in linear regime (Vds =50mV)

11

Ballistic transport (no scattering) Interferences of coherent waves

Scattering with phonons. Incoherent transport

-0.5 0 0.510-8

10-6

10-4

10-2

100

ENERGY [eV]

DIST

RIBU

TIO

N [-]

DrainMid-channel

Fermi-Dirac distribution of occupied / unoccupied electrons

𝑓= 1/1+ 𝑒↑𝐸−𝐸↓𝐹 /𝑘↓𝐵 𝑇    

à extraction of quasi-Fermi level Ef.

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

0

1

2

3

4

5x 10-3

<FER

MI L

EVEL

> n (eV)

POSITION (µ m)

ChannelAccess Access

Q=1.3e13/cm2

Q=2e12/cm2

NEGF

Hydrodynamics

Access Region: Quasi-Fermi Level 12

1/3 ‘Lost’ in Access

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

1013

1014

<DEN

SITY

> /c

m2

POSITION (µ m)

Q=2e12/cm2

Q=1.3e13/cm2

•  The Near-Spacer region exhibts a clear and large Quasi-Fermi-Level voltage drop. •  The diffusive part of the channel can be identified both in TCAD and NEGF

simulations •  Square resistance can be calculated from the derivative of the QLF vs position.

Outlook





13

Theory of Access resistance 14

-0.04 -0.03 -0.02 -0.01 0 0.010

1

2

3

4

5

6x 104

SQUA

RE R

ESIS

TANC

E (Ω

per

squ

are)

POSITION (µ m)

1: Drain

4: Channel

VG-VTH = 0.06V

VG-VTH = 0.6V

2: Drain Corner

3: Spacer

NFDSOI square resistance along current path for VG-VTH=0.06V up to VG-VTH=0.6V; VDS=0.05V.

-0.04 -0.03 -0.02 -0.01 0 0.01 0.020

1000

2000

3000

4000

5000

6000

7000

POSITION (µ m)

SQUA

RE R

ESIS

TANC

E (Ω

per

squ

are)

Spacer

Spacer

Spacer

L=22nm

L=28nm

The near-spacer resistive region does not depend on L but depends on VG

BOX

Gate Drain Source

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

50

100

150

200

250

300

350

400

450

500

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m] TCAD: σ = 33

R0 =18

Quantum (RQ/2): σ = 8.4

{ } 02)(2)(

1 RVV

R BLDDTHG

acc ⋅++⋅⋅−

= σσ

Act as Access resistance

Outlook





15

Impact of R0 on linear Drain current 16

DDTHGDTHG

OX VVVVVVV

CLI )2/())2/(1(

0 −−−−⋅+

⋅=⋅

θµ

DDTHG

DTHGOX

OX VVVVVVV

LCRCLI )2/(

))2/()2(1( 0

0 −−−−⋅

⋅⋅⋅++

⋅=⋅

µθ

µ

R0

Impact of R0 only? … or

Measured @ VD=50mV

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16x 10-6

NORM

ALIZ

ED C

URRE

NT (A

): I*L

/W

GATE VOLTAGE (V)

LCH=0.9 µmLCH=1.8 µm

LCH=0.45 µm

LCH=0.15 µm

LCH=50 nm

LCH=20 nm

µ0(L) due to additional mecanisms?

))2/(1(0

DTHGeff VVV −−⋅+=

θµ

µ

Access resistance:

Channel Mobility: L-dependent Mobility degradation

(θ :Mobility degradation parameter)

Y function[1]: deembeding for θ and R0 17

DDTHG

DTHGOX

OX VVVVVVV

LCRL

CI )2/())2/()2(1( 0

0 −−−−⋅

⋅⋅⋅++⋅

⋅=

µθ

µ

gmIY D=

LCOXeff 0µβ =

)(0THGD

OX VVVLCY −⋅=

µ

Y-function slope

[1] F. Balestra, et al., proc. ESSDERC C4 (1988).

[1]

From slope calculated at a given VG-VTH overdrive one can extract the mobility

Y function measured in NFDSOI @ VD=50mV

0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3x 10-6

Y .

(L)1/

2 FU

NC

TIO

N [S

.I.]

GATE VOLTAGE [V]

Long Devices

Short Devices

10-2 10-1 100 10160

80

100

120

140

160

180

200

EXTR

ACTE

D µ o [c

m2/V

/s]

L [µ m]

FIT: σ = 31 µ0 =0.019 Cox =0.025

Back to the equation 18

10 )(22 −−⋅⋅+⋅= THG VVRR σ

σµβ 21 0 += OXY CL

DDTHG

DTHGOXOX

OX VVVVVVV

LCR

LCL

CI )2/())2/()2(21( 000

0 −−−−⋅

⋅⋅⋅++

⋅⋅⋅+⋅

⋅=

µθ

µσµ

Access Resistance:

LCOXeff ⋅⋅+= σµµ 211 0

The extracted mobility depends on L

gmIY D=

Y-function slope

)(111 0 Beff L µµµ ⋅+=1)2( −⋅⋅= OXBB Cσµ

or

0 0.5 1 1.5 20

1000

2000

3000

4000

5000

6000

Ron Ω

. µ

m

L (µ m.)

An link bw Racc and Channel mobility?

(Linear) { } 000

22)(

1)(

1 RVVCVVC

LRTHGOXTHGOX

on ⋅+⋅⋅−

+⎭⎬⎫

⎩⎨⎧

+−

⋅= σµθ

µ

Better to think with resistance than currents:

LCOXeff ⋅⋅+= σµµ 211 0

The apparent mobility degradation is linked to the access resistance VG dependence.

10-2 10-1 100 10160

80

100

120

140

160

180

200

EXTR

ACTE

D µ o [c

m2/

V/s]

L [µ m]

FIT: σ = 31 µ0 =0.019 Cox =0.025

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

100

200

300

400

500

600

700

800

VG - VTH (V)EX

TRAC

TED

RESI

STAN

CE [ Ω

. µ

m]

Racc: σ = 31 R0 =56

RCH (L=0.018 µ m): µ 0 = 0.022

RQ/2

Raccess

TCAD: σ=33 R0=18

Apparent mobility degradation: Measurements 20

Bulk vs FD NFD vs PFD NFD vs T NFD vs Tox

LCOXeff ⋅⋅+= σµµ 211 0 σ ~ 25 - 60

)(111 0 Beff L µµµ ⋅+=

Fit:

µΒ~ 6.7- 8.3 cm2/(V.s.nm) (NMOS) Small Ballistic Mobility per unit length but in-line with other researsh group results

[e.g. µΒ~ 1.8 – 9.9 cm2/(V.s.nm) in M. Zilli, et al., Electron Device Lett. 28, 1036 (2007).]

All Devices have homogenous channel processes (no pockets,…)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7100

200

300

400

500

600

700

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m]

FDSOI: σ = 25 R0 =69

Bulk: σ = 46 R0 =33

-0.4 -0.2 0 0.2 0.4 0.6100

200

300

400

500

600

700

800

900

1000

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m]

NFDSOI: σ = 25 R0 =69

PFDSOI: σ = 58 R0 =1.6e+002

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7100

150

200

250

300

350

400

450

500

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m]

T=25°C: σ = 25 R0 =69

T=85°C: σ = 29 R0 =83

T=-40°C: σ = 24 R0 =66

0 0.2 0.4 0.6 0.8 1 1.2 1.4100

200

300

400

500

600

700

800

900

1000

1100

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m]

Cox=0.025: σ = 25 R0 =69

VD 1.8V: σ = 9.2e+002 R0 =2.4e+002VD 1.8V: σ = 9.2e+002 R0 =2.4e+002

Cox=0.01: σ = 67 R0 =1.3e+002

10-2 10-1 100 10160

80

100

120

140

160

180

200

220

EXTR

ACTE

D µ o [c

m2/

V/s]

L [µ m]

FDSOI: σ = 25 µ0 =0.021

Bulk: σ = 46 µ0 =0.02

10-2 10-1 100 10120

40

60

80

100

120

140

160

180

200

220

EXTR

ACTE

D µ o [c

m2/

V/s]

L [µ m]

NFDSOI: σ = 25 µ0 =0.021

PFDSOI: σ = 58 µ0 =0.0069

10-2 10-1 100 10150

100

150

200

250

300

EXTR

ACTE

D µ o [c

m2/

V/s]

L [µ m]

T=25°C: σ = 25 µ0 =0.021

T=85°C: σ = 29 µ0 =0.016

T=-40°C: σ = 24 µ0 =0.03

10-2 10-1 100 10150

100

150

200

250

300

350

400

EXTR

ACTE

D µ o [c

m2/

V/s]

L [µ m]

Cox=0.025: σ = 25 µ0 =0.021

Cox =0.01: σ = 67 µ0 =0.037

10 )(22 −−⋅⋅+⋅= THG VVRR σ

Key ingredients : a realistic picture for the Smaller Devices in Linear Regime

21

1

Channel length

SOI BOX

Spacer

Leff

2 3-4

1: R0

3: spacer σLDD

.(VG-VLDD)-1

3: Quantum σB.(VG-VTH)-1

4: Channel Leff

.(µeff.COX )-1.(VG-VTH)-1

HDD

Racc :Access Resistance RCH: Channel Resistance

Access: 1.  Contact Resistance (R0) 2.  Quantum Resistance 3.  Near-Spacer-region

Resistance

In general in optimized technologies L~ Leff

4/ No need for additional mecanisms in the Channel to account for the measurements:

Ron = Racc + RCH*L

Outlook





22

More NEGF simulations: Current 23

0.2 0.4 0.6 0.8 10

1000

2000

3000

4000

5000

6000

Voltage [V]

Cur

rent

[A/m

]

BalisticACAC + OP AC + OP + SR

0.2 0.4 0.6 0.8 10

200

400

600

800

1000

1200

1400

Voltage [V]

Effect of phonons

VDS = 0.9 V VDS = 50 mV

Effect ofscatterings

Effect ofscatterings

L= 20nm

More NEGF simulations: Velocity saturation

•  Saturation of velocity in long-channel FDSOI due to optical phonons is well described with NEGF.

24

0 2 4 6 8x 106

0

2

4

6

8

10

12x 104

LONGITUNAL FIELD [V/m]

VELO

CIT

Y [m

/s]

NEGF -- EMANEGF -- KP2

µ=0.055m2/(Vs)ν = 1.1e5m/s

µ=0.07m2/(Vs)ν = 1.4e5m/s

Fit with Canali model

NEGF: # Lattice parameter (nm).ACELL = 0.5431 nm# Molar mass (g/mol).MASS = 28.0855 g/mol# Longitudinal sound velocity (m/s).VL = 9000 m/s.# Transverse sound velocity (m/s).VT = 5400 m/s.# Conduction band acoustic deformation potential (eV).DAC = 14.6 eV# Number of g-type phonons.NGTYP = 3# Energies of g-type phonons (eV).EGTYP1 = 0.012 eVEGTYP2 = 0.019 eVEGTYP3 = 0.062 eV# Deformation potentials of g-type phonons (eV/Ang).DGTYP1 = 0.5 eV/AngDGTYP2 = 0.8 eV/AngDGTYP3 = 11.0 eV/Ang# Number of f-type phonons.NFTYP = 3# Energies of f-type phonons (eV).EFTYP1 = 0.019 eVEFTYP2 = 0.047 eVEFTYP3 = 0.059 eV# Deformation potentials of f-type phonons (eV/Ang).DFTYP1 = 0.3 eV/AngDFTYP2 = 2.0 eV/AngDFTYP3 = 2.0 eV/Ang

More NEGF simulations: High VD Occupied LDOS map in saturation regime (Vds =0.9V) 25

Ballistic (no scattering) Scattering with phonons Incoherent transport

-0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3

10-10

100

Energy [eV]

Den

sity

[m-2

eV-1

]

AC onlyAC + OP

At the source

At the drain

φs

φd

Opt Ph still play a role in 20nm FDSOI NFet

More NEGF simulations: details 26

-30 -20 -10 0 10 20 300

0.5

1

1.5

2

2.5

3

3.5x 105

X POSITION [nm]

VELO

CIT

Y [m

/s]

LinearSaturation

-30-25-20-15-10 -5 0 5 10 15 20 25 30

-0.8

-0.6

-0.4

-0.2

0

X POSITION [nm]

QU

ASI F

ERM

I LEV

EL [e

V]

BALPHPH+SR

-30-25-20-15-10 -5 0 5 10 15 20 25 30-0.05

-0.04

-0.03

-0.02

-0.01

0

X POSITION [nm]

QU

ASI F

ERM

I LEV

EL [e

V]

PHPH + SRBAL

-30 -20 -10 0 10 20 30

1013

1014

X POSITION [nm]

CH

ARG

E D

ENSI

TY [c

m-2

]

SaturationLinear

Charge and velocity Quasi Fermi Level

50mV

0.9V

NEGF: EMA

Velocity overshoot

Outlook





27

P&S in saturation • Current without Resistance

))/(1/()/1/( 00 AVVQQ THGci ϕθµµµ −−⋅+=+=

)/( AVVCQ THGoxi ϕ−−⋅=

)1/( * yveff ∂∂⋅+=ϕµ

µµ

)(1)(1∫∫ ⋅∂=

∂∂

⋅∂=D

s

D

s

ieffieff QLy

QyL

Iϕ

ϕ

µϕϕ

µ

)1())/(1(

)/(

*

0

yvAVV

yAVVC

ITHG

THGox

∂∂⋅+⋅−−⋅+

∂∂⋅−−⋅

=ϕµ

ϕθ

ϕϕµ

))/(1(

)/(1)1(1 0

0*

0 AVVy

AVVCy

LyvIy

L THG

THGoxLL

ϕθ

ϕϕµ

ϕµ−−⋅+

∂∂⋅−−⋅

⋅∂=∂∂⋅+⋅⋅∂ ∫∫

∫ −−⋅+−−

⋅∂=D

sAVV

AVVLCI

THG

THGoxϕ

ϕ ϕθϕ

ϕµ

))/(1()/(0

0

))/(1/( AVV THG

D

s

ϕθϕδϕ

ϕ

−−⋅+∂= ∫

⎥⎦

⎤⎢⎣

⎡

−−⋅+−−⋅+

=−−⋅+∂∫ )/(1)/(1ln))/(1/(AVVVAVVVAAVV

DTHG

STHGTHG

D

sθθ

θϕθϕ

ϕ

ϕ

θδµ )/1(0

0DSDSox VV

LCI −

⋅=

)1(

)/1(

*0

0

δµ

θ

δµ

Lv

VVLCI DSDSox

+

−⋅=

Current accounting for theta, Vsat

yAVVCI THGox ∂

∂⋅−−⋅=ϕ

ϕµ )/(0

DDTHGox VAVVVCI ⋅−−⋅= )2/(0µ

AVVV THGDsat ⋅−= )(

20 )(

2 THGoxsat VVACI −⋅⋅= µ

P&S in saturation • Current with Resistance

)1(

)/1(

*0

0

δµ

θ

δµ

Lv

VVLCI DSDSox

+

−⋅=

R=60*2, sigma=30, theta=0.1 Vsat=2.1e5m/s

IRVIRVV

S

extDD

⋅=

⋅−=

Calculation of Vdsat is numerical

10-2 10-1 100 1010.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

VDSA

T (V

)

CHANNEL LENGH (µ m)

VGT=0.5V

VGT=0.8V

VGT=0.2V

(v*, θ,R)(v*, θ)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

2

4

6

8

10

12

14x 104

RESI

STAN

CE (Ω

. µ

m)


VGT=0.2V

VGT=0.5V

VGT=0.8V

VD=1V

⎥⎦

⎤⎢⎣

⎡

−−⋅+−−⋅+

=)/(1)/(1lnAVVVAVVVA

DTHG

STHG

θθ

θδand

Approximation on VDSAT 30

•  Total Resistance @ high VD 2.σeff

⎭⎬⎫

⎩⎨⎧

+−

+⋅−

+⎭⎬⎫

⎩⎨⎧

−⋅

⋅⋅+

−⋅−

⋅⋅=

OXTHGTHG

D

THGOX

D

THGTHGOX

Don CvVV

RVVV

VVCV

VVVVCVLR *0

00

1)()(

2)(

2)()(

2 σµ

θµ

Channel ‘current’

0*00

22)(

1)2/(

1 RCvV

VVCVVVCLR

OX

D

THGOXDTHGOXon ⋅+

⎭⎬⎫

⎩⎨⎧

+⋅⋅−

+⎭⎬⎫

⎩⎨⎧

+−−

⋅= σµθ

µ

•  Total Resistance @ low VD

0.2 0.4 0.6 0.8

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

RESI

STAN

CE (Ω

. µ

m)


VD 0.05V:

VG 0.675

VD 1V

Using P&S ModelUsing Ron Approximation

0.02 0.04 0.06 0.08 0.10

200

400

600

800

1000

1200

1400

1600

1800

RESI

STAN

CE (Ω

. µ

m)


VD 0.05V:

VG 0.675

VD 1V

Using P&S ModelUsing Ron Approximation

Zoom

Diffusive Model vs NEGF 31

COX=0.025;MU0=0.069;Vsat=2.1e5;R=0; sigma=13; theta=.001;

0 0.05 0.1 0.15 0.2 0.25 0.3

500

1000

1500

2000

2500

3000

3500

RESI

STAN

CE (Ω

. µ

m)



VD 0.8V: Mean Error = 4 %

Using P&S ModelUsing Ron ApproximationNEGF

VD=10mV

VD=0.8VVGT=0.22V

VD=0.8VVGT=0.15V

VD=0.8VVGT=0.41V

0 0.1 0.2 0.3 0.4 0.50

500

1000

1500

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

[ Ω . µ

m]

VD 0.01V: σ = 13 R0 =4.9

VD 0.8V: σ = 1.1e+002 R0 =19

⎭⎬⎫

⎩⎨⎧

+−

+⋅−

==OXTHGTHG

D

CvVVR

VVVLR *0

1)()(

2)0( σ

0* 22)(

1)0( RCvV

VVLR

OX

D

THG

⋅+⎭⎬⎫

⎩⎨⎧

+⋅⋅−

== σ

Velocity overshoot (NEGF Vsat (EMA) =1.4e5 m/s)

No L-dependence in Vsat here

Diffusive Model or Virtual Source Model*? 32

0 0.05 0.1 0.15 0.2 0.25 0.3

500

1000

1500

2000

2500

3000

3500

RESI

STAN

CE (Ω

. µ

m)




Using MVS ModelNEGF

VD=10mV

VD=0.8VVGT=0.41VVD=0.8V

VGT=0.22V

VD=0.8VVGT=0.15V

COX=0.025;MU0=0.06 ;vsat=1.2e5;R=0; sigma=13;

A fit with VSM seems not so easy: è Any suggestions?

•  Injection velocity / Saturation velocity

•  Virtual Source / Pinch Off

*Trans on Electron Device Vol 62 Sept 2015

Outlook





33

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 104

Ron Ω

. µ

m

L (µ m.)






VD 1V: Mean Error = 1.4 %

0 0.05 0.1

500

1000

1500

2000

VD 0.05V: Mean Error = 4.8 %VD 0.24V: Mean Error = 3 %



34 •  Total Resistance @ high VD

2.σeff

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

500

1000

1500

2000

VG - VTH (V)

CH

AN

NE

L R

ES

ISTA

NC

E (L

=0.0

204 µ

m) [Ω

. µ

m ]

VD 0.24V: µ linext = 0.022 θ =0.0062

VD 0.43 V: µ satext = 0.016 θ ext =0.46

VD 0.62 V: µ satext = 0.023 θ ext =0.18

VD 0.81 V: µ satext = 0.023 θ ext =0.17

VD 1 V: µ satext = 0.023 θ ext =0.17

VD 0.05V: µ linext = 0.024 θ =0.0047

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

500

1000

1500

2000

2500

VG - VTH (V)

EX

TRA

CTE

D R

ES

ISTA

NC

E [ Ω

. µ

m]

VD 0.05V: σ = 30 R0 =53

VD 0.24V: σ = 59 R0 =37

VD 0.43V: σ = 76 R0 =83

VD 0.62V: σ = 1.3e+002 R0 =52

VD 0.81V: σ = 1.7e+002 R0 =72

VD 1V: σ = 2.1e+002 R0 =80

⎭⎬⎫

⎩⎨⎧

+−

+⋅−

+⎭⎬⎫

⎩⎨⎧

−⋅

⋅⋅+

−⋅−

⋅⋅=

OXTHGTHG

D

THGOX

D

THGTHGOX

Don CvVV

RVVV

VVCV

VVVVCVLR *0

00

1)()(

2)(

2)()(

2 σµ

θµ

FDSOI GO1

Measurements

Channel ‘current’

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

200

400

600

800

1000

1200

EXTR

ACTE

D PA

RAM

ETER

: σ

DRAIN VOLTAGE (V)

GO1 GO2

Current Break Down: GO1/GO2 25°C 35

0.4 0.5 0.6 0.7 0.8 0.9 1

2

4

6

8

10

x 10-5

NORM

ALIZ

ED C

HANN

EL C

URRE

NT (A

)

GATE VOLTAGE (V)0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.5

1

1.5

2

x 10-5

NORM

ALIZ

ED C

URRE

NT (A

)

GATE VOLTAGE (V)

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0

1

2

3

x 10-4

NORM

ALIZ

ED C

HANN

EL C

URRE

NT (A

)

GATE VOLTAGE (V)0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.5

1

1.5

2

2.5

3

3.5

4

x 10-5

NORM

ALIZ

ED C

URRE

NT (A

)

GATE VOLTAGE (V)

GO1

GO2

0.1 0.2 0.3 0.4 0.5 0.60

1000

2000

3000

4000

5000

VG - VTH (V)

EXTR

ACTE

D RE

SIST

ANCE

@ L

=0 [ Ω

. µ

m]

Temperature 36

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

2000

4000

6000

8000

10000

12000

14000

16000

Ron Ω

. µ

m

L (µ m.)

VGT 0.575

T= -40°C

T= 125°C T= 85°C

T= 0°C

T= 25°C

0.02 0.03 0.04 0.05 0.06 0.07

1000

1200

1400

1600

1800

0.5 0.6 0.7 0.8 0.90

2

4

6

8

10

x 10-5

SHO

RT D

EVIC

E NO

RMAL

IZED

CHA

NNEL

CUR

RENT

(A)

GATE VOLTAGE (V)

T= -40°C

T= 85°C

T= 125°C

T= 0°C

T= 25°C

0.2 0.4 0.6 0.8 1

0.5

1

1.5

2

x 10-5

SHO

RT D

EVIC

E NO

RMAL

IZED

CUR

RENT

(A)

GATE VOLTAGE (V)

T= 25°C

T= 125°C

T= 85°C

T= 0°C

T= -40°C

VD=1V

⎭⎬⎫

⎩⎨⎧

+−

+⋅− OXTHGTHG

D

CvVVR

VVV

*01

)()(2 σ

⎭⎬⎫

⎩⎨⎧

−⋅

⋅⋅+

−⋅−

⋅⋅

)(2

)()(2

00 THGOX

D

THGTHGOX

D

VVCV

VVVVCVL

µθ

µ

Velocity Saturation 37

0 0.2 0.4 0.6 0.8 10

100

200

300

400

500

600

EXTR

ACTE

D σ

DRAIN VOLTAGE (V)

T=-40 °CT=-25 °C

T=125 °C

-40 -20 0 20 40 60 80 100 120 1400.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2x 105

TEMPERATURE (deg)

SATU

RATI

ON

VELO

CITY

(m/s

)

Conclusions

1.  TCAD and NEGF comparison with a focus on the LDD-region

2.  Ron Resistance breakdown: •  Ron = Raccess (50-70%) + Rch (30-50%) •  Extraction methods should be interpreted with care

3.  LDD-region drives a large part of Ron 1.  TCAD but also NEGF clear highlight the near LDD region on the total resistance

of the device

4.  Saturation Regime 1.  P&S or VS model? 2.  Velocity Saturation 3.  Not accounted for Velocity overshoot

38

drain current in silicon-based bulk and utbb- fdsoi ... · the channel only: quantum resistance 7 2...

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