l.selmi , p.palestri, d.esseni, l.lucci, m.de michielis
DESCRIPTION
An efficient, mixed semiclassical/quantum mechanical model to simulate planar and wire nano-transistors. L.Selmi , P.Palestri, D.Esseni, L.Lucci, M.De Michielis DIEGM-IUNET, University of Udine [email protected]. Gate. Drain. Source. Current. Substrate. - PowerPoint PPT PresentationTRANSCRIPT
An efficient, mixed semiclassical/quantum
mechanical model to simulate planar and wire nano-transistors
L.Selmi, P.Palestri, D.Esseni,
L.Lucci, M.De MichielisDIEGM-IUNET, University of Udine
SLONANO 2007 L.Selmi, University of Udine
Gate
Substrate
Source DrainCurrent
FET switches: the workhorse of electronics
SLONANO 2007 L.Selmi, University of Udine
FET Technology Boostersin the ITRS roadmap [public.itrs.net]
BULK
STRAIN
Alternative Materials
Alternative Architectures
High-K
high μ
Materials &Architec.
SLONANO 2007 L.Selmi, University of Udine
Decoupling lateral transport and transverse quantization
Strong size and bias induced quantization in the vertical direction (z)
kx
ky
VS
x
E
S D
Little or no quantization in the transport plane (x-y) but …..
L
VD
VG1
VG2
VS
SLONANO 2007 L.Selmi, University of Udine
Carrier motion in the channel
Source
Ballistictransport
Real deviceIdeal device
Quasi ballistic transport: few scatterings determine the current
Modeling and simulation needs to be enhanced to deal with the key innovations requested by the PIDS section, including enhanced mobility, high-k dielectrics, metal gate electrodes, non classical CMOS […]
Modeling and simulation needs to be enhanced to deal with the key innovations requested by the PIDS section, including enhanced mobility, high-k dielectrics, metal gate electrodes, non classical CMOS […]
ITRS 2005 Edition
SLONANO 2007 L.Selmi, University of Udine
nano-FET modeling approaches• Drift Diffusion or Hydrodynamic models
– commercial tools– inadequate for nano-FETs
• Monte Carlo solver of the 3D BTE– far from equilibrium transport– no vertical or lateral quantization effects
• N.E.G.F.– 2D quantization in real space– computationally heavy– difficult to include all relevant scattering mech.
• Multi-Subband Monte Carlo (MSMC)– accurate treatment of vertical quantization– efficient semiclassical treatment of far from equilibrium transport
– computationally affordable
SLONANO 2007 L.Selmi, University of Udine
VD
VG1
xzVG2
VS
Multi subband Monte Carlo
• Boltzman Transport EquationBoltzman Transport Equation in transport directionSchrSchrödinger ödinger EquationEquationin quantization direction
• Solve 1D Schr1D Schröödingerdinger equation in each section of the device
• Solve the BTEBTE in each subband
• The solution of the BTEs are coupledcoupled by scatterings
zz
SLONANO 2007 L.Selmi, University of Udine
Schroedinger equation
•SchrÖdinger-like equation:
•Energy dispersion versus k:
xixx
zxzV
dz
d
m)()(
2 2
22
y
y
x
x
ii
m
k
m
kxxE
22)(),(
2222 k
VD
VG1
VG2
•my, mx, mz expressed in terms of mt and ml of bulk crystal
xz
y
Subband “i”
Subband “j”
X
x
xxF i
ix
)(
)(,
•Force:
SLONANO 2007 L.Selmi, University of Udine
Band Structure (electrons)
Non-parabolic elliptical bands:– Any number of , L, valleys – Strain: additional valley splitting
• Arbitrary crystal orientation:– Subbands with different quantization and transport
masses
• Various semiconductor materials implementedSi, Ge …
Effective mass approximationEffective mass approximation
SLONANO 2007 L.Selmi, University of Udine
Extraction of band parameters
UTB silicon (Tsi=5nm), (001)
Full Band LCBB calculation
For a given device:
• parametric representation of the bands at a given bias
• extraction of eff. masses
SLONANO 2007 L.Selmi, University of Udine
BTE in quantized systems
','''
',''' )',(),',(1),,(),'(),,(1),',(
kk
kr
kkStkrftkrfkkStkrftkrf
fFq
fvt
f
: sub-band index Dim(K) <3
• A BTE for each sub-band:
• Sub-bands are coupled by inter-subband scattering• Degeneration implemented by rejecting the scattering according to the occupation of the final state
SLONANO 2007 L.Selmi, University of Udine
Scattering Theory of the 2D gas
• Phonons (Price, 1980)• Ionized impurities (Ando, 1983)• Surface roughness (Esseni, 2003)• S.O.phonons in high-k materials
• Matrix elements and scattering rates computed from eigenvalues and wave-functions
• Fermi Golden Rule
• Anisotropic scattering (SR, II) is screened with the dielectric function of the 2D electron gas
SLONANO 2007 L.Selmi, University of Udine
MonteCarlo(BTE)
Poisson Equation (2D)
Schrödinger equation (1D)
Scattering Theory 2D elecron gas
Potential V(x,z)
Eigenstates ni(z) EniScattering
Rates
electron density n(x,z)
Model flowchart
SLONANO 2007 L.Selmi, University of Udine
Degeneration in thin film SOI
• degeneration plays a major role UTB MOSFETs
VD
VG1
xz
VG2
VS
)z(
ky
kx
kVS
SLONANO 2007 L.Selmi, University of Udine
Ballistic transport
Phonon scattering in source and drain,no scattering in the channel
DG SOI, NS/D=5 1020,
EOT 0.7nm, Lg=14nm,
Tsi=4nm
transport plane (x-y)
kx
ky
S D
SLONANO 2007 L.Selmi, University of Udine
Transport with scattering
Phonon scattering in source and drain,Phonon, Surface roughness and Tsi Fluctuations in the channel
DG SOI, NS/D=5 1020,
EOT 0.7nm, Lg=14nm,
Tsi=4nm
transport plane (x-y)
kx
ky
S D
SLONANO 2007 L.Selmi, University of Udine
Mobility: effect of surface orientation
• Same model parameters of (001) and (111) orientations
• Adjustment of SR spectrum for (110)
[Lucci, IEEE T-ED, p.1156, 2007]
SLONANO 2007 L.Selmi, University of Udine 18
Transport in biax. strained-Si devices
TRANSPORT DIRECTIONTRANSPORT DIRECTION
QUANTIZATION QUANTIZATION DIRECTIONDIRECTION
SLONANO 2007 L.Selmi, University of Udine 19
Mobility in biax. strained-Si devices
CB=0.67x [eV] [Rashed, IEDM 1995]
SLONANO 2007 L.Selmi, University of Udine
Extension to nanowire FETs
SLONANO 2007 L.Selmi, University of Udine
What are we missing ?• Surface roughness / interface effects• Tunneling through the Source barrier• Scattering mechanisms• Atomistic effects
sourcesource
3 nmdraingate
oxide
SLONANO 2007 L.Selmi, University of Udine
Conclusions• A new Monte Carlo code based on the theory of
the two dimensional carrier gas has been developed for n- and p-type MOSFETs
• Quasi ballistic transport in ultra thin body DG SOI devices has been investigated
• Importance of a correct modeling of scattering in the channel and of carrier degeneration has been highlighted
• The modularity of the code and the parametric description of the band structure make the simulator suitable for extensions to devices with different channel material and crystal orientation
SLONANO 2007 L.Selmi, University of Udine
Acknowledgements
• EU Nestor (5FP), SiNano (6FP), PullNano (6FP) projects
• Italian FIRB 2001 and PRIN 2004 projects
• MS and PhD students: Nicola Barin, Marco Nicola Barin, Marco Braccioli, Simone Eminente, Andrea Ghetti, Braccioli, Simone Eminente, Andrea Ghetti, Davide Ponton, Ivan Riolino, Massimiliano Davide Ponton, Ivan Riolino, Massimiliano Zilli and all the IU.NET – ARCES partnersZilli and all the IU.NET – ARCES partners
SLONANO 2007 L.Selmi, University of Udine
Device modeling approaches
Drift Diffusion
Hydrodynamic
Classical (3D) Monte Carlo
Green’s Function
CommComm
UnivUniv / /CommComm
UnivUniv
Fu
nd
amen
tal
Th
eory
of
tran
spo
rtNear Near EquilibriumEquilibrium
DisplacedDisplacedMaxwellianMaxwellian
BoltzmannBoltzmannTransport eq.Transport eq.
Schrodinger eg.Schrodinger eg.
Ver
tica
lq
uan
tiza
tio
n
(Density(Densitygradientgradientcorrection)correction)
(Density(Densitygradientgradientcorrection)correction)
(S/D (S/D tunnelingtunnelingcorrection)correction)
IncludedIncludedD
egen
erat
ion
PossiblePossible
NONO
YESYES
Bal
listi
ctr
ansp
ort
NONO
NONO
YESYES
YESYES
Vel
oci
ty
ove
rsh
oo
t
Multi Sub Band Monte Carlo
Univ Univ BTE 2D +BTE 2D +SE 1DSE 1D IncludedIncluded YESYES YESYES
NONO
YESYES
YESYES
YESYES
YESYES
Sca
tter
ing
, v, vss
YESYES
YESYES
Fu
ll B
and
NONO
NONO
YESYES
YESYES
NONO
Lat
eral
qu
anti
zati
on
IncludedIncluded
(S/D (S/D tunnelingtunnelingcorrection)correction)
(Effective(Effectivepotentialpotentialcorrection)correction)
Su
b-t
hre
sho
ld
YESYES
YESYES
PossiblePossible
Ava
ilab
ility
PhonPhon YESYES
CommComm
, v, vss
TT
PossiblePossible
PossiblePossible
PossiblePossible
PossiblePossible