T02_Iannaccone_MOS_AK_Rome

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G. Iannaccone Universit di Pisa

!!Electrostatics:"!Multiple gates and undoped body"!Degeneracy"!Strain (and its dependence on geometry)

!!Transport:

#!Partially ballistic transport!!Noise:

"! Noise in the case of partially ballistic transport!!Variability modeling

"! Support the designers


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!!Transport:





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!!G. Baccarani, S. Reggiani,TED 46, 1656 (1999)."! Double gate MOSFET"! Doped body"! Quantum confinement"! Degenerate electron gas"! Non quasi-static effects"! DD transport

!!Y. Taur, EDL 21, 245 (2000)"! Double gate MOSFET"! Undoped body"! No quantum confinement"! DD transport


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!!D. Jimenez et al. EDL 25,314 (2004)"! GAA (cylindrical) MOSFET"! Degenerate 1D electron gas"! Ballistic transport [in EDL 25,

571 (2004) DD transport)]

!!H. Abd El Hamid et al. TED54, 2487 (2007)"! Trigate MOSFET"! Semiclassical model"! Subthreshold behavior


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!!Transport:





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!!A. Rahman, M. Lundstrom, TED 49, 481 (2002).

r: backscattering coefficient

ID: net drain current


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!!A. Rahman, M. Lundstrom, TED 49, 481 (2002).

Assumptions:

#!single sub-band (E1)#!I+ = IBallistic#!n+ = nBallistic#!v+ = v- = vth (elastic scattering)n+ (n-): positive (negative) directed carrier concentration (cm-2)

v+ (v-) : carrier velocity of positive (negative) directed currenth=(EFS-E1)/kT


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!!A. Rahman, M. Lundstrom, TED 49, 481 (2002).!!Critical aspects:

"! Strong assumptions"! Cannot be connected seamlessly

with the DD transport model (is aFirst order perturbation with

respect to ballistic transport)

!!Advantages:"! Very simple $ all is captured in r


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Consistently with the

approach of Buttikerprobes [Buttiker,1986], a drift-diffusion MOSFET canbe seen as a chain

of ballistictransistors. .

NMOSFETs $ current continuity imposes Nequations forthe Nunknowns:-!N-1: internal Fermi levels V

k(k = 1, , N-1)

-!1 : drain currentG. Mugnaini, G. Iannaccone, TED 52, 1795 (2005), TED 52, 1802 (2005)


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!! If N is sufficiently large(i.e. the voltage drop on allballistic channels is smaller than the thermal voltage)"! DD current-voltage characteristics are obtained (EKV-like), with

!! If the voltage drop on some transistors of the ballisticchain is larger than the thermal coltage:"! DD current with field-dependent

mobility


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When non-linear transport emerges, it

manifests its effects mainly in the last

ballistic transistor of the chain.


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!!The DD: length L-!, with velocity saturation!!B: fully ballistic device!!Can seamlessly cover the transition from ballistic to

long channel.


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!!Extended to silicon nanowire FETs, carbon nanotubes,graphene nanoribbon FETs:"! P. Michetti et al., TED 56, 1402 (2009)

!!Extended to one dimensional FETs with Schottkybarrier contacts (P. Michetti, G. Iannaccone, TED 2010)


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!!Transport:#!Partially ballistic transport

!!Noise:"! Noise in the case of partially ballistic transport

!!Variability modeling"! Support the designers


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!!B. Cheng, SSE 49, 740 (2005),SISPAD 2009

!!Statistical simulations ofRDD,LER,PGG variability yieldan ensemble of devices withdifferent electrical properties

!!For each devices one extracts aset of 7 BSIM parameters $ astatistical set of BSIMparameters is obtained

!!Correlation between BSIMparameters is reproduced

!!Linearity is not required.


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!! V. Bonfiglio, G. Iannaccone, ESSDERC 2009!! All variability sources (process and geometry) are

translated in terms of the dispersion of a number ofsynthetic parameters

!! Independent variability sources are identified!! The contribution to the dispersion of electrical

parameters (e. g. Vth) of each independent source is

evaluated through sensitivity analysis


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!!Hypothesis quantities of interest: y1, y2, x1, x2, x3"!are only affected by LER and SR"!are physically independent


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!!LER described by 1D exp. autocorrelation function"!correlation lenght !L and mean square amplitude "L


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Vds= 50 mV("S= 0.15 nm, !S= 1.8 nm)("L = 1.3 nm, !L = 25 nm)

Approach

Fully

Analytical

Analytical +TCAD

AtomisticGlasgow

(Cheng et al.)

32 nm

#VthLER(mV) 2.96 3 3.3#VthSR(mV) 0.23 0.25 N/A

22 nm

#Vth

LER(mV) 6 5.6 5.8#VthSR(mV) 1.4 1.4 N/A


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Vds= 1 V("S= 0.15 nm, !S= 1.8 nm)("L = 1.3 nm, !L = 25 nm)

Approach

Fully

Analytical

Analytical +TCAD

AtomisticGlasgow

(Cheng et al.)

32 nm#VthLER(mV) 7.9 8.3 8.6#VthSR(mV) 0.66 0.6 N/A

22 nm

#VthLER(mV) 14 13.6 13#VthSR(mV) 4.3 4.4 N/A


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!!X. Li et al. IEEE-TCAD 29, 599 (2010)"!ei (i=1,m): measures of electrical performance"!pj (i=1,n): process parameters (independent)

!!m equations in n unknown (m>n$ least square fit)!! are obtained from experiments

"!$ can be extracted for Monte Carlo!!Critical aspect:pj are assumed independent!!Test show that linearization works.

"ei

2=

#ei

#pj

$

%&&

'

())

2

"p j

2

j=1

n

*

"ei

2

"p j

2

Obtained

from PSP


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!!Transport:#!Partially ballistic transport

!!Noise:"! Noise in the case of partially ballistic transport

!!Variability modeling"! Support the designers


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?

Acknowledgments:

FP7 NoE NANOSIL (n. 216171), ENIAC project 12003 MODERN

T02_Iannaccone_MOS_AK_Rome

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