G. Iannaccone Università di Pisa
G. IannacconeUniversità 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 beyondCMOS and beyond
G. Iannaccone Università di Pisa
AcknowledgmentsAcknowledgments
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
Silicon Nanowire Transistors (SNWT)Silicon Nanowire Transistors (SNWT)
G. Iannaccone Università di Pisa
x
nqD
x
EnqJ i
i
Dn
iDnni
11
The 3D electron density is obtained as :
Transport models in the 1D Transport models in the 1D subbandssubbands
Two models for current1. Ballistic transport in each subband (including
tunneling)2. Drift-Diffusion transport in each 1D subband (Ei).
(note: The mobility model must be improved).1D subband profiles
2nd
3rd
4th
1st
n3D i
2n1Dii
G. Iannaccone Università di Pisa
SNWT simulated structures : same transversal cross-section (5x5 nm, 1.5 nm
oxide) different channel lengths (L=7,10,15,25 nm)
Simulation of SNWT (I)Simulation of SNWT (I)
G. Iannaccone Università di Pisa
Simulation of SNWT (II)Simulation of SNWT (II)
Electrostatic potential in a y-z cross section in the middle of the channel :
Vds = 0.5 V ; Vgs = 0.5 V
Electron Density Isosurface n=1.4x1019cm-3; L=15 nm; Vgs=0.5 V; Vds=0.5V
source
draingate
G. Iannaccone Università di Pisa
Simulation of SNWT (III)Simulation of SNWT (III)
S degrades for small L but is still acceptable and almost insensitive to the transport mechanism
DIBL is much higher for ballistic than for DD transport.
G. Iannaccone Università di Pisa
Silicon Nanowire Transistors (IV)Silicon Nanowire Transistors (IV)
Source-drain tunneling above threshold gives a contribution only slightly dependent on L , and significant already for L=25 nm.
G. Iannaccone Università di Pisa
High-k dielectricsHigh-k dielectrics
Lead: Andrea Campera
G. Iannaccone Università di Pisa
Structures investigatedStructures investigated
Experimental data: I-V, C-V and I(T)-V In all three cases the substrate is p-doped with NA=5∙1017 cm-3
C-V characteristics have been measured for capacitors of area 70 µm x 70 µm
J-V curves have been measured for n-MOSFET with W=10 µm and L=1, 5 and 10 µm ( we show results only for L=5 µm)
Temperature from 298 to 473 K
SiO2
HfO2
Poly-Si
bulk
4 nm1 nm SiON
HfSiONPoly-Si
bulk
2 nm1 nm SiON
HfSiONPoly-Si
bulk
1 nm1 nm
EOT a) 1.7 nm b) 1.6 nm c) 1.3 nm
G. Iannaccone Università di Pisa
1D Poisson-Schrödinger solver1D Poisson-Schrödinger solver
Poly depletion and finite density of states in the bulk
2
2
1 exp2( ) ln
1 exp
1 exp4( ) ln
1 exp
Fl ilt ril il
Fr ili
Fl itt l rit it
Fr iti
E E kTqkTJ m T E
E E kT
E E kTqkTm m T E
E E kT
Self-consistent solution of the P-S equation, taking into account quantum confinement at the
emitter, quantum confinement in the poly mass anisotropy in CB, light and heavy holes
Extraction of the band profile with the quasi-equilibrium approx., eigenvalues and eigenvectors for electrons and holes
G. Iannaccone Università di Pisa
Results: I-V and C-VResults: I-V and C-V
summary of physical parameters extracted for HfO2 , HfSiON and SiON
HfO2 HfSiON SiON
Electron affinity 1.575 eV 1.97 eV 1.27 eV
Electron eff mass
0.08m0 0.24m0 0.45m0
r 25 11 5
FLP 0.35 V 0.13 V -
G. Iannaccone Università di Pisa
Experiment: Temperature-dependent Experiment: Temperature-dependent I-VI-V
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
Gavartin, Shluger, Foster, Bersuker Jour.Appl. Phys 2005
G. Iannaccone Università di Pisa
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
G. Iannaccone Università di Pisa
TransconductanceTransconductance
G. Iannaccone Università di Pisa
IIoff per unit width
the Ion/Ioff requirement is met for a tube density smaller than 0.1
G. Iannaccone Università di Pisa
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
G. Iannaccone Università di Pisa
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.
G. Iannaccone Università di Pisa
Bulk nMOSFETs: Inverse Bulk nMOSFETs: Inverse ModellingModelling
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
nominal value) Channel doping Polysilicon Doping LDD, HDD, pocket implant doping
G. Iannaccone Università di Pisa
Inverse ModellingInverse Modelling
-1.0 -0.5 0.0 0.5 1.0
0.006
0.008
0.010
0.012
0.014
0.016
ND=1.2 x 1020 cm-3
Experiment NANOTCAD2D
Cap
acita
nce
[F/m
2 ]V
GS [V]
0.0 0.1 0.2 0.3 0.41
2
3
4
5
Dose=6.7*1013 atoms/cm2
Bor
on p
rofil
e [x
1018
cm
-3]
x [nm]
-50 -40 -30 -20 -10 0 10 20 30 40 50
1E18
1E19
1E20L
eff=26nm
degenerate doping level
Dop
ing
[cm
-3]
y [nm]
Long device C-V and I-V
experimental characteristics are used.
Accumulation and low-inversion C-V and I-V used to extract the doping profile in the well.
Donor concentration in the poly extracted from the strong-inversion C-V curve.
Short device Fitting with C-V & I-V
characterization. The doping of pockets,
HDDs and LDDs has been fitted with a Gaussian function
G. Iannaccone Università di Pisa
PLI1043 Process (T10-T07-T05-PLI1043 Process (T10-T07-T05-T04)T04)
0.0 0.2 0.4 0.6 0.8 1.0
1E-4
1E-3
0.01
0.1
1
10
100
1000
LG=200 nm (T07)
Cur
rent
[A/m
]
VGS
[V]
Experiment NANOTCAD2D
-0.2 0.0 0.2 0.4 0.6 0.8 1.01E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
1000
LG=64 nm (T05)
Cur
rent
[A/m
]
VGS
[V]
Experiment NANOTCAD2D
0.2 0.4 0.6 0.8 1.01E-5
1E-4
1E-3
0.01
0.1
1
10
100
LG=880 nm (T10)
Cur
rent
[A/m
]
VGS
[V]
Experiment NANOTCAD2D
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.01E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
1000
LG=40nm (T04)
Cur
rent
[A/m
]
VGS
[V]
Experiment NANOTCAD2D
G. Iannaccone Università di Pisa
0.0 0.2 0.4 0.6 0.8 1.00
100
200
300
400
500
600
VDS
= 0.05,0.55,1.05 V
Cur
rent
[A/m
]
VGS
[V]
Experiment DD per subband
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.01E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
1000
Cur
rent
[A/m
]
VGS
[V]
Experiment DD per subband
64nm nMOSFET (50 nm L64nm nMOSFET (50 nm Leff))
Extracted effective channel lenght: Leff=50nm
Capability to reproduce experimental results both in sub-threshold and in strong-inversion conditions.
Behavior in strong inversion requires that extension resistances are included in the simulation
Note: Electrostatics is more important than the mobility model !!
G. Iannaccone Università di Pisa
-0.2 0.0 0.2 0.4 0.6 0.8 1.00
200
400
600
800
1000
VDS
= 0.05, 0.55, 1.05 V
Cur
rent
[A/m
]
VGS
[V]
Experiment DD per subband
-0.6 -0.3 0.0 0.3 0.6 0.91E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
1000
Cur
rent
[A/m
]
VGS
[V]
Experiment DD per subband
Extracted effective channel lenght: Leff=25nm
Capability of reproducing experimental results in the sub-50nm regime.
Comparison with DESSIS-Synopsys. Simulation time comparable.
-0.2 0.0 0.2 0.4 0.6 0.8 1.00
200
400
600
800
1000
VDS
= 0.05, 0.55, 1.05 V
Cur
rent
[A/m
]
VGS
[V]
Experiment NANOTCAD2D DESSIS
40nm nMOSFET (25 nm L40nm nMOSFET (25 nm Leff))
G. Iannaccone Università di Pisa
In the ballistic device a series (extension and overlap) resistance RDS = 110 m has been considered
Extracted velocity:
The ballistic efficiency is about 50%
The 25nm bulk-Si MOSFET roughly operate at 50% of its ballistic limit.
0.00 0.25 0.50 0.75 1.000
200
400
600
800
1000
1200
1400
1600
Cur
rent
[A/m
]
VGS
[V]
Experiment Ballistic + R
SD=110 ohm-um
scmv
scmv
ball
eff
/1035.1
/1022.77
6
Ballistic EfficiencyBallistic Efficiency
G. Iannaccone Università di Pisa
Nanocrystal and discrete-trapNanocrystal and discrete-trapFlash memoriesFlash memories
Lead: G. Fiori
G. Fiori et al., APL, vol. 86, 113502 (2005)
In collaboration with LETI, IMEC, STM (now in the FinFlash project)
G. Iannaccone Università di Pisa
M. Saitoh, E. Nagata, and T. Hiramoto, Appl. Phys. Lett., Vol. 82,
No. 11, 2003
Such behavior has been related to the presence of percolating paths in the channel
Nanocrystal memories on SOI wiresNanocrystal memories on SOI wires
G. Iannaccone Università di Pisa
Device fabricationDevice fabrication
Device Cross-Section
BOX
Control gate
Control oxide
A-A’
n+ n+Si-filmBOX
Control gate
Control oxide
B-B’
Si-film
DUVDUV E-beam
SiBOX
8” SOI wafers
A
B’B
A’
Realized by G. Molas, B. De Salvo, CEA-LETI
G. Iannaccone Università di Pisa
Experimental results (LETI)Experimental results (LETI)
The effect is also observed in the strong inversion regime, when percolating paths cannot possibly be present.
G. Iannaccone Università di Pisa
50nm
S DW
Actual and simulated geometryActual and simulated geometry
S D
Poly gate
G. Iannaccone Università di Pisa
Discrete charge distribution in the dot layer Discrete charge distribution in the dot layer (I)(I)
We have then considered a discrete distribution of fixed charge in the dot layer.
Average dot density is 5x1011 cm-2.
Electron density isosurface n=1018 cm-3
computed for VGS=1.6 V
n+
dot layer
L
W
SiO2
xy
z
gate
G. Iannaccone Università di Pisa
Discrete charge distribution in the dot layer Discrete charge distribution in the dot layer (II)(II)
strong inversion sub-threshold
Threshold voltage shift over a sample of twelve devices with the same nominal dot density, but with a different discrete distribution of charged dot
G. Iannaccone Università di Pisa
Stored charge Stored charge local tunnel current density local tunnel current density (I)(I)
Since dots are charged by direct tunneling current, we have assumed the fixed charge density proportional to the direct tunneling current.
W = 30 nm
W = 80 nm
Electron density isosurface n=7.5x1023m-3 computed for VGS=-0.4 V, in case of charged and discharged dots.
discharged dots
charged dots
G. Iannaccone Università di Pisa
The assumption that the stored charged is proportional to the local current density, allows us to reproduce the experiments behavior
Stored charge Stored charge local tunnel current local tunnel current density (II)density (II)
G. Iannaccone Università di Pisa
““Rounded” structure (2D)Rounded” structure (2D)
This effect is also present also if the structure does not have sharp edges. Consider the minimum curvature structure
Above threshold
Sub-threshold
G. Fiori et al., APL, vol. 86, 113502 (2005)
G. Iannaccone Università di Pisa
Effect of a Finite Curvature at the Effect of a Finite Curvature at the edgeedge
63 nm
20 nm
63 nm
20 nm
local tunnel current density along the Si/SiO2 interface
SONOS FinFET structure with round fin edges. Simulation with Silvaco ATLAS + Post processing with in-house tools Curvature radius of 5 nm and 10 nm.
-80 -60 -40 -20 0 20 40 60 80100
101
102
103
104
105
106
curvature radius=10 nm
curvature radius=5 nm
Cu
rren
t D
ensi
ty (
A/m
2 )
Curvilinear Coordinate (nm)
Current is injected mainly
at the edges
G. Iannaccone Università di Pisa
Experimental CV-CurvesExperimental CV-Curves From long devices:
extraction of doping profile in the well.
Quantum confinement must be considered both in the polysilicon layer and in the channel.
Region1: Schrödinger
Region2: Potential at the
poly/SiO2 interface is increased due to quantum effects Negative shift of the threshold voltage
-10 -8 -6 -4 -2 0 2 4
0.8
1.0
1.2
1.4
Poly Quantum No Poly Quantum
Pot
entia
l [V
]
x [nm]0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Ele
ctro
n D
ensi
ty [x
1023
m-3]
x [nm]
Schrödinger + Drift-DiffusionSchrödinger + Ballistic Model
Poly SiO2 Si
G. Iannaccone Università di Pisa
Co/Ti
Rcsd Rdeep Rext Rov
Rcsd= contact resistance
Rdeep= HDD resistanceRdeep= extension resistanceRov= overlap resistance
Quantum Box
Series ResistanceSeries Resistance
0.00 0.25 0.50 0.75 1.000
50
100
150
200
LG=40nm (T04)
Cur
rent
[A/m
]
VGS
[V]
Experiment W=10nm W=40nm W=50nm W=180nm
Contact resistance and deep HDD resistance are not included in the simulation.
Overlap and extension resistances considered adjusting the lateral dimension on the quantum region where continuity eq. is solved.
G. Iannaccone Università di Pisa
NanoTCAD2DNanoTCAD2D2D Poisson
ii) i) ii) iii)
i) +
+
+
Quantum Bohm Potential (QBP)
1D SchrödingerBallistic Model (BM)
Drift-diffusion per subband (DDS)
1D Schrödinger2D Schrödinger
The Schrödinger equation must be solved twice for each slice: For the 2 minima along the vertical (kx) direction
For the other 4 minima
lililiClil
yE~Ey,xxmx
1
2
2
tititiCtit
yE~Ey,xxmx
1
2
2
TkEE~
explnTmk
nB
Flili
tBli 12
2
Tk
EE~expln
mmTkn
B
Ftiti
tlBti 12
2kx
ky
kz
kx
kz
ky
G. Iannaccone Università di Pisa
Uniform stored charge in the dot Uniform stored charge in the dot layerlayer
The average dot density is 5x1011cm-2. As a first attempt, we have modelled the dot layer
as a uniform fixed charge layer Different behavior from experiments
n+
gate
dot layer
L
W
SiO2
xy
z
G. Iannaccone Università di Pisa
Direct Tunneling CurrentDirect Tunneling Current
i i
tili nnn 42
The current density is larger in correspondence of the corner of the structure.
),( bEJ The direct tunnel current is a
function of the electric field (E) and of the barrier heigth (Φb)
G. Iannaccone Università di Pisa
63 nm
20 nm
Transfer characteristics from 3D Transfer characteristics from 3D simulationsimulation
Curvature radius 5nm
Vth shift of about 0.5 V and dependent on
Effect of the stored charge on Vth shift
The transfer characteristics are not simply shifted
Assumption of locally stored charge proportional to the local Injected tunnel current-1 0 1 2 3 4
10-10
10-9
10-8
10-7
10-6
10-5
10-4
0 1 2 3 4
20
40
60
80
100
Cu
rren
t (A
)
Gate Voltage (V)
Fresh Cell
=3x1019 cm-3
=1020 cm-3
Cu
rren
t (
A)
Gate Voltage (V)
G. Iannaccone Università di Pisa
63 nm
20 nm
Electron concentration at the Si-SiO2 Electron concentration at the Si-SiO2 interfaceinterface
0 10 20 30 40 50 60 701010
1012
1014
1016
1018
1020
1022
Vg=1.0 V
Vg=2.0 V
Vg=3.0 V
Vg=4.0 V
Ele
ctro
n C
once
ntra
tion(
cm-3)
Curvilinear Coordinate (nm)
The stored charge inhibits channel formation ONLY at the edges The programmed device behaves as the parallel of
a low Vth fresh device (channel at the flat fin surface) and a very high Vth device (channel at the fin edges).
0 10 20 30 40 50 60 7010-610-410-2100102104106108
1010101210141016101810201022
Vg=1.0 V
Fresh Cell
=3x1019cm-3
=1020cm-3
Ele
ctro
n C
once
ntra
tion
(cm
-3)
Curvilinear Coordinate (nm)
Programmed cell r=5 nm