physics-based compact model for ultimate finfets -...

Physics-based compact

model for ultimate FinFETs

[email protected]

Ashkhen YESAYAN, Nicolas CHEVILLON, Fabien PREGALDINY,

Morgan MADEC, Christophe LALLEMENT, Jean-Michel SALLESE

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


Outline

Mobility modeling3

Short-channel effects modeling2

Introduction1

Quantum mechanical effect modeling4

Transcapacitance modeling5

Doped DG MOSFET modeling6


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

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.


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


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.


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

[2]


Study of the minimum surface potential

Cross-section

of FinFET

Study in:

- classic physics

- weak inversion


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

Correction of the gate voltage:

Drain current model:




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


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




Quantum mechanical effects [1] (1/3)

Quantum shift of the first energy level:



E0

WSi

E1

EC

Structural confinement

E0

E1

WSi

EC

Electrical confinement

Principle of the quantum mechanical effects modeling


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


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


Results of the static model

Id(Vd) current curves

Symbols: Quantum 3D simulations with CVT mobility model

Lines: Compact model

Id(Vg) current curves


Transcapacitance modeling [1]

Normalized total charge calculation according to the

channel charge partition proposed by Ward

Transcapacitance definitions:



Charge-based expressions for the transcapacitances


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




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


Doped DG MOSFET model [1]

The equivalent-thickness concept

Including the doping Na in the

Poisson’s equation,

Energy diagram


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



we obtain a similar model than the

one for the undoped DG MOSFET [2].


Doped DG MOSFET model [1]

The equivalent-thickness concept

Charge-potentials relationship




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


Doped DG MOSFET results

Drain current versus gate voltage

Normalized drain current


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.




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

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.

physics-based compact model for ultimate finfets -...

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