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Physics-based compact model for ultimate FinFETs [email protected] Ashkhen YESAYAN, Nicolas CHEVILLON , Fabien PREGALDINY, Morgan MADEC, Christophe LALLEMENT, Jean-Michel SALLESE
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Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

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Page 1: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

Physics-based compact

model for ultimate FinFETs

[email protected]

Ashkhen YESAYAN, Nicolas CHEVILLON, Fabien PREGALDINY,

Morgan MADEC, Christophe LALLEMENT, Jean-Michel SALLESE

Page 2: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK2

Research team and collaboration

Professor - Christophe LALLEMENT

Associate professor - Fabien PREGALDINY

Associate professor - Morgan MADECCompact modeling

of advanced devicesPost-doc – Ashkhen YESAYAN - left in Dec. 2010

PhD student - Nicolas CHEVILLON

Collaboration

Dr. Jean-Michel SALLESE

LEG, EPFL

Page 3: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK3

Outline

Mobility modeling3

Short-channel effects modeling2

Introduction1

Quantum mechanical effect modeling4

Transcapacitance modeling5

Doped DG MOSFET modeling6

Page 4: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK4

FinFET transistor

One of the best candidate to extend the CMOS technology.

Needs of designers for advanced circuit simulation:

(COMON European project)

• a physics-based FinFET compact model

• a parameter extraction methodology

L: channel length

WSi: silicon width

HSi: silicon height

tox: oxide thickness

Page 5: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK

Model accounts for small-geometry effects [3]:

• Short-channel effects (SCE), drain-induced barrier lowering (DIBL)

• Subthreshold swing degradation

• Drain saturation voltage and channel length modulation (CLM)

• Mobility degradation

• Quantum mechanical effects (QME)

5

Physics-based FinFET compact model

Physics-based long-channel DG MOSFET model [1]

• Extension of the undoped model to high doping [2]

[1] J.-M. Sallese, F. Krummenacher, F. Prégaldiny, C. Lallement, A. Roy and C. Enz, “A design oriented charge-based current model for

symmetric DG MOSFET and its correlation with the EKV formalism,” Solid-State Electronics, vol. 49, no. 3, pp.485-489, Mar 2005.

Transcapacitance modeling for small-geometry [3]

[3] A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for ultra-scaled FinFETs,”

Solid-State Electronics, Article in Press, April 2011.

[2] J.-M. Sallese, N. Chevillon, F. Prégaldiny, C. Lallement and B. Iñiguez, “The equivalent-thickness concept for doped symmetric DG

MOSFETs,” IEEE Transactions on Electron Devices, vol. 57, no. 11, pp.2917-2924, Nov 2010.

Page 6: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK6

Range of validity

Gate length (L) : down to 25 nm

Silicon width (WSi) : down to 3 nm

Silicon height (HSi): down to 50 nm

Gate oxide thickness (tox) : 1.5 nm

Top oxide thickness (ttop) : 50nm

Channel doping (Nch) : intrinsic to 1017 cm-3 and high doping*

Source/Drain doping (Nsd) : 51021 cm-3

*: only for long channel devices

Page 7: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK7

Long channel drain current model [1]

Normalized drain current:

Normalized charge-potentials relationship:

[2] F. Prégaldiny, F. Krummenacher, B. Diagne, F. Pêcheux, J.-M. Sallese and C. Lallement “, Explicit modelling of the double-gate

MOSFET with VHDL-AMS” Int. J. Numer. Model., vol. 19, pp. 239-256, Mar 2006.

[1] J.-M. Sallese, F. Krummenacher, F. Prégaldiny, C. Lallement, A. Roy and C. Enz, “A design oriented charge-based current model for

symmetric DG MOSFET and its correlation with the EKV formalism,” Solid-State Elec., vol. 49, no. 3, pp.485-489, Mar 2005.

[2]

Page 8: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK8

Study of the minimum surface potential

Cross-section

of FinFET

Study in:

- classic physics

- weak inversion

Page 9: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK9

Current model for ultra-short channels [1] (1/2)

Correction of the gate voltage:

Drain current model:

[1] A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for ultra-scaled FinFETs,”

Solid-State Electronics, Article in Press, April 2011.

Page 10: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK10

Current model for ultra-short channels (2/2)

Potential Expression in the channel in the subthreshold region [1]:

[1] X. Liang, and Y. Taur, “A 2-D Analytical solution for SCEs in DG MOSFETs,” IEEE Trans. Electron Devices, vol. 51, no. 8, pp. 1385-

1391, August 2004.

In weak inversion:

• in the long-channel case,

• in the short-channel case,

In strong inversion, analytical expression is negligeable w.r.t ,

No need of smoothing function between weak and strong inversion.

valid for L > 1.5 SiW

General scaling length

Page 11: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK11

Mobility model [1]

Term of mobility degradation

for the short channels in

weak inversion

Terms of mobility degradation

in strong inversion

: long-channel low field mobility

: transversal electric field in weak inversion

: transversal electric field in high inversion

: parameters to be extracted

[2] F. Lime, B. Iñiguez and O. Moldovan, “A quasi-two dimentional compact drain-current model for undoped symmetric double-gate

MOSFETs including short-channel effects,” IEEE Trans. Electron Devices, vol. 55, no. 6, pp. 1441-1448, June 2008.

Transversal mobility:

Total mobility model and channel length modulation model taken from [2]

: normalizing factor

[1] A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for ultra-scaled FinFETs,”

Solid-State Electronics, Article in Press, April 2011.

Page 12: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK12

Quantum mechanical effects [1] (1/3)

Quantum shift of the first energy level:

[1] A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for ultra-scaled FinFETs,”

Solid-State Electronics, Article in Press, April 2011.

E0

WSi

E1

EC

Structural confinement

E0

E1

WSi

EC

Electrical confinement

Principle of the quantum mechanical effects modeling

Page 13: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK13

Quantum mechanical effects (2/3)

Inclusion of the term of structural confinement in the

charge-potential relationship

Inclusion of the term of electrical confinement

in the charge-potential relationship

Modeling of the quantum shift as a correction to surface potential:

: elementary electronic charge

: thermal voltage

: effective mass of electrons in the channel length direction

Page 14: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK14

Quantum mechanical effects (3/3)

New charge-potentials relationship:

Normalized drain current expression:

Addition of a term in the drain

current expression by taking into

account the QMEs

Page 15: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK15

Results of the static model

Id(Vd) current curves

Symbols: Quantum 3D simulations with CVT mobility model

Lines: Compact model

Id(Vg) current curves

Page 16: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK16

Transcapacitance modeling [1]

Normalized total charge calculation according to the

channel charge partition proposed by Ward

Transcapacitance definitions:

[1] A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for ultra-scaled FinFETs,”

Solid-State Electronics, Article in Press, April 2011.

Charge-based expressions for the transcapacitances

Page 17: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK17

Transcapacitance modeling [1]

Modeling of the electrical confinement by approximated according

to a taylor series,

Modeling of the structural confinement by in

the calculation of the charge density .

within a new definition of the gate oxide capacitance

[1] A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for ultra-scaled FinFETs,”

Solid-State Electronics, Article in Press, April 2011.

Page 18: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK18

Results of the dynamic model

Symbols: Quantum 3D simulations with constant mobility

Lines: Compact model

Cgg(Vg) of long channel Cgg(Vg) of short channel

Page 19: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK19

Doped DG MOSFET model [1]

The equivalent-thickness concept

Including the doping Na in the

Poisson’s equation,

Energy diagram

[2] J.-M. Sallese, F. Krummenacher, F. Prégaldiny, C. Lallement, A. Roy and C. Enz, “A design oriented charge-based current model for

symmetric DG MOSFET and its correlation with the EKV formalism,” Solid-State Electronics, vol. 49, no. 3, pp.485-489, Mar 2005.

[1] J.-M. Sallese, N. Chevillon, F. Prégaldiny, C. Lallement and B. Iñiguez, “The equivalent-thickness concept for doped symmetric DG

MOSFETs,” IEEE Transactions on Electron Devices, vol. 57, no. 11, pp.2917-2924, Nov 2010.

we obtain a similar model than the

one for the undoped DG MOSFET [2].

Page 20: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK20

Doped DG MOSFET model [1]

The equivalent-thickness concept

Charge-potentials relationship

[1] J.-M. Sallese, N. Chevillon, F. Prégaldiny, C. Lallement and B. Iñiguez, “The equivalent-thickness concept for doped symmetric DG

MOSFETs,” IEEE Transactions on Electron Devices, vol. 57, no. 11, pp.2917-2924, Nov 2010.

Page 21: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK21

Doped DG MOSFET results

Equivalent thickness Mobile charge density

Exact analytical relationship between the equivalent thickness and the doping

Tsi = 40 nm

20 nm

10 nm

Page 22: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK22

Doped DG MOSFET results

Drain current versus gate voltage

Normalized drain current

Page 23: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK23

Electrical parameter number of the model

Effect Previous model [1,2] Present model [3]

Roll-off (SCE), DIBL

Subthreshold Slope (SS)

18 0

Channel Length

Modulation (CLM)

1 1

Mobility - 2

Quantification (QME) 9 0

Overlap capacitance - 1

All 28 4

[1] M. Tang, F. Prégaldiny, C. Lallement, J.-M. Sallese, “Explicit compact model for ultranarrow body FinFETs” IEEE Trans. Electron

Devices, vol. 56, no. 7, pp.1543-1547, Jul 2009.

[2] N. Chevillon, M. Tang, F. Prégaldiny, C. Lallement et M. Madec, “FinFET compact modeling and parameter extraction,” 16th IEEE

MIXDES., pp.55-60, Juin 2009.

[3] A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for ultra-scaled FinFETs,”

Solid-State Electronics, Article in Press, April 2011.

Page 24: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

N. CHEVILLON [email protected] 8 April 2011MOS-AK24

Conclusion

SCE & DIBL

Sub-threshold Slope degradation

Drain saturation voltage

Channel length modulation (CLM)

Mobility degradation

Quantum mechanical effects

Extrinsic capacitances

Included effects

Validity range

ID(VGS) & ID(VDS), small-signal parameters (gm, gds, …)

L ≥ 25nm

WSi ≥ 3 nm

HSi= 50nm

tox= 1.5nm

Perspectives

Physic-based modeling of the temperature dependence

3D modeling: consideration of the triple-gate FinFET

Extension of the doped model to short-channel devices

Parameter extraction methodology associated with an

automated extraction procedure

Page 25: Physics-based compact model for ultimate FinFETs - MOS-AKmos-ak.org/paris/papers/P09_Chevillon_MOS-AK_2011.pdf · Physics-based compact model for ultimate FinFETs ... B. Diagne, F.

A. Yesayan, F. Prégaldiny, N. Chevillon, C. Lallement and J.-M. Sallese, “Physics-based compact model for

ultra-scaled FinFETs,” Solid-State Electronics, Article in Press, April 2011.

J.-M. Sallese, N. Chevillon, F. Prégaldiny, C. Lallement and B. Iñiguez, “The equivalent-thickness concept

for doped symmetric DG MOSFETs,” IEEE Transactions on Electron Devices, vol. 57, no. 11, pp.2917-2924,

Nov 2010.

Major publications:

J.-M. Sallese, F. Krummenacher, F. Prégaldiny, C. Lallement, A. Roy and C. Enz, “A design oriented charge-

based current model for symmetric DG MOSFET and its correlation with the EKV formalism,” Solid-State

Electronics, vol. 49, no. 3, pp.485-489, Mar 2005.