G. Iannaccone Università di Pisa G. Iannaccone Università di Pisa and IU.NET [Italian Universities Nanoelectronics Consortium] Via Caruso 16, I-56122, Pisa, Italy. [email protected]Nanoscale Device Nanoscale Device Modelling: Modelling: CMOS and beyond CMOS and beyond
Nanoscale Device Modelling: CMOS and beyond. G. Iannaccone Università di Pisa and IU.NET [Italian Universities Nanoelectronics Consortium] Via Caruso 16, I-56122, Pisa, Italy. [email protected]. Acknowledgments. People that did (are doing) the “real” work - PowerPoint PPT Presentation
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G. Iannaccone Università di Pisa
G. IannacconeUniversità di Pisa
and IU.NET [Italian Universities Nanoelectronics Consortium]
People that did (are doing) the “real” work A. Campera, P. Coli, G. Curatola, G. Fiori, F. Crupi,
G. Mugnaini, A. Nannipieri, F. Nardi, M. Pala, L. Perniola Partners
IMEC, LETI, STM, Silvaco (EU FinFlash Project) Univ. Wuerzburg, ETH Zurich, TU Vienna, MPG Stuttgart,
NMRC Cork (EU NanoTCAD Project) EU Sinano NoE (43 partners) Next: PullNANO IP IU.NET Italian Universities Nanoelectronics Corsortium Univ. Bologna, Univ. Udine, Univ. Roma (PRIN
Programme) Philips Research Leuven, Purdue University, Univ.
Illinois at Urbana Champaign, Samsung Funding (past and present)
European Commission, Italian Ministry of University, Italian National Research Council, Foundation of Pisa Savings Bank, Silvaco International
G. Iannaccone Università di Pisa
The ProblemThe Problem
“Yesterday’s technology modeled tomorrow”
(M.E.Law, 2004)
TCAD and numerical modeling tools – both for process and device simulation – are accurate, or “predictive”, only for a sufficiently stable and “mature” technology, and after a lengthy calibration procedure.
G. Iannaccone Università di Pisa
Modeling as a Strategic ActivityModeling as a Strategic Activity
Modeling is a strategic activity because it enables to
perform an early evaluation of technology options
make choices and cut unpromising initiatives
strategically position and focus R&D efforts
Modeling supports the definition and the
implementation of a R&D strategy
G. Iannaccone Università di Pisa
Emerging Research Devices
Nanocrystal and discrete trap flash memories
Quantum dots and single electron transistors
CNT-FETs Resonant Tunneling
Devices
Fundamentals of Nanoelectronics
Decoherence and dephasing
Spin-dependent transport Mesoscopic transport
ITRS Roadmap Issues Quantum ballistic and
quasiballistic modeling of nanoscale MOSFETs (2D-3D)
Alternative device structures (DG MOSFETs, FINFETs, SNWTs)
Tunneling currents through oxides and high-k gate stacks, also in the presence of defects (SILCs, etc.)
Atomistic effects in nanoscale MOSFETs
Compact modeling of nanoscale MOSFETs
Present activity in PisaPresent activity in Pisa
G. Iannaccone Università di Pisa
ITRS Roadmap Issues Quantum ballistic and
quasiballistic modeling of nanoscale MOSFETs (2D-3D)
Alternative device structures (DG MOSFETs, FINFETs, SNWTs)
Tunneling currents through oxides and high-k gate stacks, also in the presence of defects (SILCs, etc.)
Atomistic effects in nanoscale MOSFETs
Compact modeling of nanoscale MOSFETs
Present activity in PisaPresent activity in Pisa
Emerging Research Devices
Nanocrystal and discrete trap flash memories
Quantum dots and single electron transistors
CNT-FETs Resonant Tunneling
Devices
Fundamentals of Nanoelectronics
Decoherence and dephasing
Spin-dependent transport Mesoscopic transport
G. Iannaccone Università di Pisa
NanoTCAD3DNanoTCAD3D
3D Non linear Poisson
1D Schrödinger per slice
Ballistic Transport
DD per each 2D subband
3D Schrödinger
The many body Schrödinger equation is solved with DFT-LDA, effective mass approximation
The Kohn-Sham equation for electrons is solved for each pair of minima in the conduction band (three times)
The Kohn-Sham equation for holes is solved for heavy and light holes
+2D Schrödinger per
section
Ballistic Transport
DD per each 1D subband
+
G. Iannaccone Università di Pisa
1Dx
z
y
2D
3D
NanoTCAD3DNanoTCAD3D
Depending on device architecture, multiple regions different types of confinement may be considered: Planar MOSFET: 1D vertical confinement Nanowire: 2D confinement in the transversal cross section Dots: 3D
Many body Schrödinger equation solved with DFT-LDA, effective mass approximation
G. Iannaccone Università di Pisa
Quantum ballistic and Quantum ballistic and quasiballistic modeling of quasiballistic modeling of nanoscale MOSFETs (3D)nanoscale MOSFETs (3D)
Lead: G. Fiori
G. Iannaccone Università di Pisa
Candidate device structures for MOSFETs with channel length of order 10 nm – Suppressed SCE
HfO2 and HfSiON shows a different temperature dependence
A pure tunneling current can explain only transport in HfSiON but not in HfO2
In HfO2 we can observe a strong temperature dependence
G. Iannaccone Università di Pisa
g1= g1c+ g1v
g2= g2c+ g2v
r1= r1c+ r1v
r2= r2c+ r2v
Temperature-dependent transport Temperature-dependent transport modelmodel
1 2 2 1
1 2 1 2TAT
g r g rJ q
g g r r
We assume that transport in HfO2 is due to Trap Assisted Tunneling
gi and ri depend on the properties of traps responsible for transport
They depend on the capture cross section, that we have assumed to be “Arrhenius like”
0 exp BE k T
The TAT current reads
G. Iannaccone Università di Pisa
Energy position of traps Energy position of traps
Traps in hafnium oxide from ab-initio calculations
From simulations we observe that traps must be within the energy range 1÷2 eV below the HfO2 conduction band in order to allow us to reproduce the shape of J-V characteristics
We consider that relevant traps are located 1.6 eV below the hafnium oxide CB
Simulations of I(V) with varying TSimulations of I(V) with varying T
0.4 0.5 0.6 0.7 0.8 0.9 1.01E-4
1E-3
0.01
0.1
1
10
=0.1 eV
=0.084 eV=0.05 eV
=0.01 eV
measured @ 475 K
Cu
rren
t d
en
sity
(A/m
2 )
Gate Voltage (V)
=0.001 eV
From ETRAP=1.6 eV we can extract Г from the slope of the J-V @ 475 K and σ(475) from the amplitude of the same J-V
At T=475 K TAT is the entire current density We assume that σ has an Arrhenius temperature
dependence and that Г is constant: Then we can extract σ as a function of temperature
320 340 360 380 400 420 440 460 480
0.0
2.0x10-7
4.0x10-7
6.0x10-7
8.0x10-7
1.0x10-6
1.2x10-6
simulated Arrhenius fit
sig
ma
(m2 J
)
Temperature (K)
infexp(-E/kT)
inf= 0.555
E=0.542 eV
0 exp BE k T
G. Iannaccone Università di Pisa
Main resultsMain results
0.4 0.6 0.8 1.010-3
10-2
10-1
100
101 theory experiments
Cu
rren
t D
ensi
ty
(A/m
2 )
Gate Voltage (V)
T from 300 to 475 K
0.5 1.0 1.5 2.0100
101
102
103
104
105
106
Experiments @ 400 K Experiments @ 300 K Theory (pure tunneling)
Curr
ent D
ensi
ty (A
/m2 )
Gate Voltage (V)
HfSiON c)
HfO2HfSiON
Transport in HfSiON can be described by pure tunneling processes Transport in HfO2 can be described by temperature dependent TAT Arrhenius like capture cross section Traps involved in transport processes are 1.6 eV below the
hafnium oxide CB (this traps states have been recently found by ab-initio calculations, Gavartin et al. Jour. Appl. Phys 2005)
G. Iannaccone Università di Pisa
Decoherence and dephasingDecoherence and dephasing
Lead: Marco Pala*
M. Pala, G. Iannaccone, PRB vol. 69, 235304 (2004)M. Pala, G. Iannaccone, PRL vol. 93, 256803 (2004)
* now with IMEP-CNRS, Grenoble
G. Iannaccone Università di Pisa
Transport in mesoscopic structuresTransport in mesoscopic structures
Landauer-Büttiker theory of transport Eigenvalues of the tt† matrix as
enables us to compute conductance and shot noise
Transmission and reflection matrices can be obtained computing the scattering matrix (S-matrix) of the system
The domain is subdivided in several tiny slices in the propagation direction
The S-matrix of the system is obtained by combining the S-matrices of all adjacent slices
n
nhe TG
22
n
nnhVe TTS )1(
32
R
L
R
L
R
L
b
a
rt
tr
b
as
a
b
'
'
G. Iannaccone Università di Pisa
Monte Carlo approach (M. Pala, G. Iannaccone, PRB 2004)
Random fluctuation of the phase of all modes
The propagation in each slice is described by a diagonal term in the transmission matrix
We modify the transmission matrix by adding a random phase to each diagonal term
The random phase has a Gaussian distribution with zero average and variance inversely proportional to the dephasing lenght
Each S-matrix is a particular occurrence and the average transport properties are obtained by averaging over a sufficient number of runs
nmxikj
nmRj
jnet
lx jj /2
G. Iannaccone Università di Pisa
Aharonov-Bohm rings
Simulation recover experimental results due to the suppression of quantum coherence
Non integer conductance steps are recovered Corrections are of the order of G0
Experiments by A.H.Hansen et al.,
PRB 2004
B=0 Tesla
G. Iannaccone Università di Pisa
MagnetoconductanceMagnetoconductance
Experiment (Hansen et al., PRB 2004)
Theory(Pala et al., 2004)
G. Iannaccone Università di Pisa
Density of statesDensity of states
Computation of the partial density of states
Application: Aharonov-Bohm oscillations of a ring
[M.G. Pala and G. Iannaccone, PRB 69, 235304 (2004)]
The wave-like behavior of the propagating mode is destroyed when a strong decoherence is present
2|),,(|),,( EyxEyx
G. Iannaccone Università di Pisa
Influence on shot noise (M. Pala et al. PRL 2004)
Aharonov Bohm ring
First order cumulant of the current proportional to conductance
Second order cumulant of the current = Fano factor (prop to noise)
G. Iannaccone Università di Pisa
Perspectives of Carbon Perspectives of Carbon Nanotube Field Effect Nanotube Field Effect
TransistorsTransistors
Lead: G. Fiori
Collaboration with Purdue University,
G. Fiori et al., IEDM 2005 – to be published on IEEE-TED, new results at ESSDERC 2006
G. Iannaccone Università di Pisa
Discretization : box-integration. Newton-Raphson method with predictor corrector scheme.
n() in the nanotube by means of NEGF
Self-consistent 3D Poisson/NEGF Self-consistent 3D Poisson/NEGF solversolver
The 3D Poisson equation reads
while p(f), ND+(f), NA-(f) e n(f) are computed semiclassically elsewhere. Transport is ballistic.
In particular, the Schrödinger equation has been solved using a tight-binding hamiltonian with an atomistic (pz-orbital) real space basis
G. Iannaccone Università di Pisa
Non-Equilibrium Green’s FunctionNon-Equilibrium Green’s Function
The Green’s Function can be expressed as
A point charge approximation is assumed, i.e. all the free charge around each carbon atoms is condensed in the elementary cell including the atom.
Current is computed through the Landauer’s formula
G. Iannaccone Università di Pisa
Short Channel Effect in CNT-FETs Short Channel Effect in CNT-FETs (I)(I)
By defining different geometries, we can study how short channel effects can be controlled through different device architectures.
Considered CNT-FET (11,0) zig-zag nanotube doping molar fraction f
= 10-3. gatelength 15 nm SiO2 as gate dielectric. single, double and triple
gate layout.
G. Iannaccone Università di Pisa
Short Channel Effect in CNT-FETs Short Channel Effect in CNT-FETs (II)(II)
Quasi-ideal S are obtained for the double gate structure, also for thick oxide thickness.
Good S and DIBL for the single gate device are obtained for tox=2nm. As expected, triple gate layout show better S and DIBL
G. Iannaccone Università di Pisa
IIon per unit width
Ion is one order of magnitude higher than that typically obtained in silicon
warning: ballistic transport and very dense CNTs considered
G. Iannaccone Università di Pisa
High frequency perspectivesHigh frequency perspectives
Optimistic estimate (zero stray capacitances)
Perspective for THz applications
High frequency behaviour is only limited by stray gate capacitance
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TransconductanceTransconductance
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IIoff per unit width
the Ion/Ioff requirement is met for a tube density smaller than 0.1
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Efs
Efd
LDOS for Vgs=0, Vds=0.6 VCharge density computed for
Vgs=0 and Vds=0.6 V
electronselectrons
holesholes
Effects of bound states in HOMO Effects of bound states in HOMO (I)(I)
For large drain-to-source voltages, electrons in bound states in the channel can tunnel to states in the drain, leaving holes in the channel. Such effect lowers the barrier seen by propagating electrons in the channel.
G. Iannaccone Università di Pisa
As the drain-to-source voltage is increased, holes are accumulated in the channel and the gate loses control of the potential over the channel, with a degradation of the current in the off-state.
Transfer characteristic for a double gate (14,0) nanotube, with L=10 nm and tox=2 nm
Effects of bound states in HOMO (II)
G. Iannaccone Università di Pisa
Work in ProgressWork in Progress
G. Iannaccone Università di Pisa
in Progress: Mobility in Si in Progress: Mobility in Si NanowiresNanowires
Phonon scattering (acousting and optical) Surface Roughness and Cross Section
Fluctuations Impurity Scattering
5 nm
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10 ps
Partially ballistic transportPartially ballistic transport
Boltzmann Transport Equation solved in each 2D subband
Direct solution (no Montecarlo)
S D
Ballistic peak
G. Iannaccone Università di Pisa
Partially ballistic transportPartially ballistic transport
Boltzmann Transport Equation solved in each 2D subband
Direct solution (no Montecarlo)
S D
Ballistic peak
1 ps
G. Iannaccone Università di Pisa
Partially ballistic transportPartially ballistic transport
Boltzmann Transport Equation solved in each 2D subband
Direct solution (no Montecarlo)
S D
Ballistic peak
1 ps
G. Iannaccone Università di Pisa
Partially ballistic transportPartially ballistic transport
Boltzmann Transport Equation solved in each 2D subband
Direct solution (no Montecarlo)
S D
1 ps
G. Iannaccone Università di Pisa
Personal ConclusionPersonal Conclusion
Critical objectives of nanoscale device modeling: Provide useful insights of device behavior, helping us to understand
what are the relevant physical aspects for the issues at hand
what are the main trends what we should focus on and what we should
stop.
Such mission does not requires huge do-it-all tools, but simulation tools with different degrees of sophistication, tailored to the particular problem at hand.
G. Iannaccone Università di Pisa
Modeling of ballistic and quasi-Modeling of ballistic and quasi-ballistic MOSFETsballistic MOSFETs
Lead: G. Curatola*
In collaboration with Philips Research Leuven,
G. Curatola et al. IEEE-TED vol. 52, p. 1851-1858, 2005
* now with Philips Research Leuven
G. Iannaccone Università di Pisa
Typical aspects of the nanoscaleTypical aspects of the nanoscale
DD1st ordermomentum
HD2nd ordermomentum
CompleteThermalization(equilib.)
SCALING DOWNTechnology GenerationTime
Fully ballistictransport
Carrier distribution in the phase space
DSmetal
Polyx
yz
L
STI
Plus: Strong confinement in the 2DEG Strong confinement in the Poly !
G. Iannaccone Università di Pisa
Drift-Diffusion per subband Drift-Diffusion per subband
Poisson Eq. + Schrödinger Eq. + Continuity Eq.
Leff
0 x
EFD
EFS
dxxx
dxxyxxy
ii
ii
i)()(
)(),()()(
*
*
F
i
inini
En
nμD
Continuity eq. is solved within each subband obtained after the solution of the 1D Schrödinger equation.
Fermi-Dirac statistics is required.
Full self-consistent approach
Approximation: Semi-empirical local
mobility model is used. The mobility in each
subband is weighted with the corresponding eigenfunction.
Modified diffusion coefficient to include Fermi-Dirac statistics.
Data (PLI1043 process) from Philips Research Leuven: Doping profile obtained with TSUPREM4 Oxide thickness Tox=1.5nm C-V and I-V characteristics Set of devices with different gate length!
Several Unknowns: Gate length (dispersion with respect to