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]
G. Iannaccone
Università di Pisa
Acknowledgments
 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 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 Activity
Modeling is a strategic activity because it enables to
early evaluation of technology options
make choices and cut unpromising initiatives
strategically position and focus R&D efforts
 perform an


Modeling supports the definition and the implementation of a R&D
strategy
G. Iannaccone
Università di Pisa
Present activity in 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
G. Iannaccone
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
Università di Pisa
Present activity in 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
G. Iannaccone
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
Università di Pisa
NanoTCAD3D
3D Non linear Poisson
1D Schrödinger per slice
+
2D Schrödinger per section
3D Schrödinger
+
Ballistic Transport
Ballistic Transport
DD per each 2D subband
DD per each 1D subband
 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
G. Iannaccone
Università di Pisa
NanoTCAD3D
2D
1D
3D
y
x
z
 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 quasiballistic
modeling of nanoscale MOSFETs (3D)
Lead: G. Fiori
G. Iannaccone
Università di Pisa
Silicon Nanowire Transistors (SNWT)
Candidate device structures for MOSFETs with channel
length of order 10 nm – Suppressed SCE
G. Iannaccone
Università di Pisa
Transport models in the 1D subbands
Two models for current
1. Ballistic transport in each subband (including tunneling)
2. Drift-Diffusion transport in each 1D subband (Ei).
(note: The mobility model must be improved).
J ni  q n n1Di
n1Di
Ei
 qDn
x
x
The 3D electron density is
obtained as :
n 3D    i n1Di
2
1D subband profiles
4th
3rd
2nd
1st
i
G. Iannaccone
Università di Pisa
Simulation of SNWT (I)
 SNWT simulated structures :
 same transversal cross-section (5x5 nm, 1.5 nm oxide)
 different channel lengths (L=7,10,15,25 nm)
G. Iannaccone
Università di Pisa
Simulation of SNWT (II)
 Electron Density Isosurface
n=1.4x1019cm-3; L=15 nm;
Vgs=0.5 V; Vds=0.5V
 Electrostatic potential in a y-z
cross section in the middle of
the channel :
Vds = 0.5 V ; Vgs = 0.5 V
G. Iannaccone
Università di Pisa
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)
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 dielectrics
Lead: Andrea Campera
G. Iannaccone
Università di Pisa
Structures investigated
4 nm
1 nm
Poly-Si
HfO2
SiO2
bulk
EOT
a) 1.7 nm
Poly-Si
2 nm HfSiON
1 nm SiON
bulk
Poly-Si
1 nm HfSiON
1 nm SiON
bulk
b) 1.6 nm
c) 1.3 nm
 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
G. Iannaccone
Università di Pisa
1D Poisson-Schrödinger solver
 Poly depletion and finite density  Self-consistent solution of the P-S
of states in the bulk
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
J

G. Iannaccone
2qkT

4qkT

2
2
mt

 1  exp  EFl  Eil  kT  



1

exp
E

E
kT


il

 Fr
 
 1  exp  EFl  Eit  kT  
 rit T ( Eit ) ln 



1

exp
E

E
kT


it
 Fr
 

 ril T ( Eil ) ln 
i
mt ml

i
Università di Pisa
10
7
10
5
10
3
10
1
90
10
HfSiON (c)
HfO2 (a)
-1
10
-3
10
-5
HfO2 (a)
Experiments
Theory
-3
-2
-1
0
1
2
3
Capacitance (pF)
2
Current density (A/m )
Results: I-V and C-V
a) HfO2
80
with FLP
70
60
50
without FLP
40
30
20
10
0.35 V
Experiments
Theory
0
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0
Gate Voltage (V)
Gate Voltage (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
25
11
5
0.35 V
0.13 V
-
er
FLP
G. Iannaccone
Università di Pisa
Experiment: Temperature-dependent I-V
 HfO2 and HfSiON shows a different temperature dependence
-2
10
1
-3
from T = 298 K
to T = 448 K
10
10
-4
10
-3
10
from T = 298 K
to T = 473 K
-5
10
-5
10
HfSiON (b)
-2
-6
10
-7
10
HfO2 (a)
2
-1
|J G (A/cm )|
2
|JG (A/cm )|
10
-7
-1
0
1
Gate Voltage (V)
2
10
-1.5
-1.0 -0.5
0.0
0.5
Gate Voltage (V)
1.0
 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
Temperature-dependent transport model
 We assume that transport in HfO2 is due to Trap Assisted Tunneling
g1= g1c+ g1v
g2= g2c+ g2v
r1= r1c+ r1v
r2= r2c+ r2v
 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   E kBT 
 The TAT current reads J TAT
G. Iannaccone
g1r2  g 2 r1
q
g1  g 2  r1  r2
Università di Pisa
Energy position of traps
 Traps in hafnium oxide from abinitio 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
Gavartin, Shluger, Foster, Bersuker Jour.
Appl. Phys 2005
 We consider that relevant traps are
located 1.6 eV below the hafnium
oxide CB
G. Iannaccone
Università di Pisa
Simulations of I(V) with varying T
 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:    0 exp  E kBT
 Then we can extract σ as a function of temperature

1.2x10
-6
1.0x10
-6
8.0x10
-7
6.0x10
-7
4.0x10
-7
2.0x10
-7
measured @ 475 K
10
=0.1 eV
=0.01 eV
2
1
sigma (m J)
2
Current density (A/m )

0.1
=0.084 eV
=0.05 eV
=0.001 eV
0.01
1E-3
infexp(-E/kT)
inf= 0.555
E=0.542 eV
simulated
Arrhenius fit
0.0
1E-4
0.4
0.5
0.6
0.7
0.8
Gate Voltage (V)
G. Iannaccone
0.9
1.0
320 340 360 380 400 420 440 460 480
Temperature (K)
Università di Pisa
Main results
HfSiON
10
10
10
10
10
theory
experiments
2
1
(A/m )
10
6
0
-1
-2
T from 300
to 475 K
-3
0.4
0.6
0.8
Gate Voltage (V)




5
10
HfSiON c)
4
10
1.0
Current Density
2
Current Density (A/m )
HfO2
3
10
Experiments @ 400 K
2
10
Experiments @ 300 K
Theory (pure tunneling)
1
10
0
10
0.5
1.0
1.5
2.0
Gate Voltage (V)
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 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 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 Smatrices of all adjacent slices
G. Iannaccone
G
2e2
h
T
n
n
S
2 e 3V
h
 T (1  T )
n
n
n


 bL   aL   r
    s    
a  b 
 R   R  t

t '  aL 
  
r '  bR 
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
G. Iannaccone
t
j
nm
e
iknj x j  R
 nm
  x j / l
2
j
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
B=0 Tesla
Experiments by
A.H.Hansen et al.,
PRB 2004
G. Iannaccone
Università di Pisa
Magnetoconductance
Experiment
(Hansen et al., PRB 2004)
G. Iannaccone
Theory
(Pala et al., 2004)
Università di Pisa
Density of states
 Computation of the partial
density of states
 ( x, y, E ) | ( x, y, E ) |2
 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
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 Nanotube Field
Effect Transistors
Lead: G. Fiori
Collaboration with Purdue University,
G. Fiori et al., IEDM 2005 – to be published on IEEETED, new results at ESSDERC 2006
G. Iannaccone
Università di Pisa
Self-consistent 3D Poisson/NEGF solver
 The 3D Poisson equation reads
n() in the nanotube by means of
NEGF
 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
 Discretization : box-integration.
 Newton-Raphson method with predictor corrector scheme.
G. Iannaccone
Università di Pisa
Non-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 (I)
 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.
 By defining different
geometries, we can study how
short channel effects can be
controlled through different
device architectures.
G. Iannaccone
Università di Pisa
Short Channel Effect in CNT-FETs (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
Ion 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 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
Transconductance
G. Iannaccone
Università di Pisa
Ioff per unit width
 the Ion/Ioff
requirement
is met for a
tube density
smaller than
0.1
G. Iannaccone
Università di Pisa
Effects of bound states in HOMO (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.
Efs
Efd
holes
electrons
LDOS for Vgs=0, Vds=0.6 V
G. Iannaccone
Charge density computed for
Vgs=0 and Vds=0.6 V
Università di Pisa
Effects of bound states in HOMO (II)
 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
G. Iannaccone
Università di Pisa
Work in Progress
G. Iannaccone
Università di Pisa
in Progress: Mobility in Si Nanowires
 Phonon scattering (acousting and optical)
 Surface Roughness and Cross Section Fluctuations
 Impurity Scattering
5 nm
G. Iannaccone
Università di Pisa
Partially ballistic transport
 Boltzmann Transport Equation solved in each 2D subband
 Direct solution (no Montecarlo)
Ballistic peak
S
D
t10 ps
G. Iannaccone
Università di Pisa
Partially ballistic transport
 Boltzmann Transport Equation solved in each 2D subband
 Direct solution (no Montecarlo)
Ballistic peak
S
D
t1 ps
G. Iannaccone
Università di Pisa
Partially ballistic transport
 Boltzmann Transport Equation solved in each 2D subband
 Direct solution (no Montecarlo)
Ballistic peak
S
D
t0.1 ps
G. Iannaccone
Università di Pisa
Partially ballistic transport
 Boltzmann Transport Equation solved in each 2D subband
 Direct solution (no Montecarlo)
S
D
t0.01 ps
G. Iannaccone
Università di Pisa
Personal 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-ballistic
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 nanoscale
Carrier distribution in the phase space
HD
2nd order
DD momentum
1st order
momentum
Complete
Thermalization
(equilib.)
SCALING DOWN
Technology
Generation
Time
 Plus:
Fully ballistic
transport
z
y
Poly
x
S
L
 Strong confinement in the 2DEG
 Strong confinement in the Poly !
metal
D
STI
G. Iannaccone
Università di Pisa
Drift-Diffusion per subband
Poisson Eq. + Schrödinger Eq. + Continuity Eq.
 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
EFS
EFD
Leff
0
x
 i ( x)  ( x, y )i ( x)dx
*
i ( y ) 
Dni  μni
 i ( x)i ( x)dx
*
ni
ni
EF
Università di Pisa
Bulk nMOSFETs: Inverse Modelling
 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 Modelling
5
-3
4
18
ND=1.2 x 10 cm
0.012
0.010
0.008
0.006
3
2
1
0.0
-1.0 -0.5 0.0 0.5 1.0
0.1
0.2
0.3
0.4
x [nm]
VGS [V]
Leff=26nm
1E20
-3
Doping [cm ]
2
0.014
2
-3
20
13
Dose=6.7*10 atoms/cm
Boron profile [x 10 cm ]
0.016
Capacitance [F/m ]
Long device
 C-V and I-V experimental
characteristics are used.
 Accumulation and lowinversion 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
Experiment
NANOTCAD2D
degenerate doping level
1E19
1E18
-50
G. Iannaccone
-40
-30
-20
-10
0
10
y [nm]
20
30
40
50
Università di Pisa
PLI1043 Process (T10-T07-T05-T04)
1000
100
Experiment
NANOTCAD2D
1
100
Current [A/m]
Current [A/m]
10
LG=880 nm (T10)
0.1
0.01
1E-3
10
1
0.1
0.01
Experiment
NANOTCAD2D
1E-3
1E-4
1E-4
1E-5
LG=64 nm (T05)
1E-5
0.2
0.4
0.6
0.8
1E-6
-0.2
1.0
0.0
0.2
VGS [V]
0.8
1.0
1000
Experiment
NANOTCAD2D
100
100
10
LG=200 nm (T07)
Current [A/m]
Current [A/m]
0.6
VGS [V]
1000
10
0.4
1
0.1
0.01
1E-3
0.2
0.4
0.6
VGS [V]
G. Iannaccone
0.1
0.01
1E-3
LG=40nm (T04)
1E-4
Experiment
NANOTCAD2D
1E-5
1E-4
0.0
1
0.8
1.0
1E-6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
VGS [V]
Università di Pisa
64nm nMOSFET (50 nm Leff)
1000
 Extracted effective channel
lenght: Leff=50nm
 Capability to reproduce
experimental results both in
sub-threshold and in stronginversion conditions.
Current [A/m]
100
Experiment
DD per subband
10
1
0.1
0.01
1E-3
1E-4
600
Current [A/m]
500
Experiment
DD per subband
1E-5
1E-6
-0.4
VDS = 0.05,0.55,1.05 V
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
VGS [V]
400
300
200
100
0
0.0
0.2
0.4
0.6
VGS [V]
G. Iannaccone
0.8
1.0
 Behavior in strong
inversion requires that
extension resistances are
included in the simulation
 Note: Electrostatics is
more important than the
mobility model !!
Università di Pisa
40nm nMOSFET (25 nm Leff)
1000
100
Current [A/m]
 Extracted effective channel
lenght: Leff=25nm
 Capability of reproducing
experimental results in the sub50nm regime.
 Comparison with DESSIS-Synopsys.
Simulation time comparable.
10
1
0.1
0.01
1E-3
1E-4
Experiment
DD per subband
1E-5
1E-6
-0.6
-0.3
0.6
0.9
1000
Experiment
DD per subband
600
400
200
0
-0.2
VDS= 0.05, 0.55, 1.05 V
600
400
200
0.0
0.2
0.4
VGS [V]
G. Iannaccone
Experiment
NANOTCAD2D
DESSIS
800
VDS = 0.05, 0.55, 1.05 V
Current [A/m]
Current [A/m]
0.3
VGS [V]
1000
800
0.0
0.6
0.8
1.0
0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
VGS [V]
Università di Pisa
Ballistic Efficiency
veff  7.22  106 cm / s
vball  1.35  107 cm / s
 The ballistic
efficiency is about
50%
 The 25nm bulk-Si
MOSFET roughly
operate at 50% of its
ballistic limit.
G. Iannaccone
1600
Experiment
Ballistic + RSD=110 ohm-um
1400
1200
Current [A/m]
 In the ballistic device
a series (extension
and overlap)
resistance RDS = 110
W m has been
considered
 Extracted velocity:
1000
800
600
400
200
0
0.00
0.25
0.50
0.75
1.00
VGS [V]
Università di Pisa
Nanocrystal and discrete-trap
Flash 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
Nanocrystal memories on SOI wires
 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
G. Iannaccone
Università di Pisa
Device fabrication
Realized by G. Molas, B. De Salvo, CEA-LETI
8” SOI wafers
DUV E-beam DUV
Si
BOX
A’
B’
B
A
Control gate
Control gate
Control oxide
n+
Si-film
BOX
A-A’
G. Iannaccone
n+
Device
Cross-Section
Control oxide
Si-film
BOX
B-B’
Università di Pisa
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
Actual and simulated geometry
Poly
gate
S
S
W
D
D
50nm
G. Iannaccone
Università di Pisa
Discrete charge distribution in the dot layer (I)
z
We have then considered a
discrete distribution of fixed
charge in the dot layer.
dot
layer
y
x
gate
W
n+
Average dot density is
5x1011 cm-2.
L
SiO2
Electron density isosurface
n=1018 cm-3 computed for
VGS=1.6 V
G. Iannaccone
Università di Pisa
Discrete charge distribution in the dot layer (II)
Threshold voltage shift over a sample of twelve devices
with the same nominal dot density, but with a
different discrete distribution of charged dot
strong inversion
G. Iannaccone
sub-threshold
Università di Pisa
Stored charge  local tunnel current density (I)
 Since dots are charged by direct tunneling current, we have assumed
the fixed charge density proportional to the direct tunneling current.
Electron density isosurface
n=7.5x1023m-3 computed for VGS=-0.4 V,
in case of charged and discharged dots.
G. Iannaccone
discharged dots
charged dots
Università di Pisa
Stored charge  local tunnel current density (II)
 The assumption that the stored charged is proportional to the local
current density, allows us to reproduce the experiments behavior
G. Iannaccone
Università di Pisa
“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 edge
10
6
10
5
10
4
10
3
10
2
10
1
curvature
radius=10 nm
curvature
radius=5 nm
2
Current Density (A/m )
 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.
local tunnel current density
along the Si/SiO2 interface
0
63 nm
63 nm
10
-80
-60
-40
-20
0
20
40
60
80
Curvilinear Coordinate (nm)
20 nm
G. Iannaccone
20 nm
Current is injected mainly
at the edges
Università di Pisa
Experimental 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.
Si
23
1.4
1.6
-3
Region1: Schrödinger
SiO2
Electron Density [x 10 m ]
Poly
Region2:
Schrödinger + Ballistic Model
 Potential at the
poly/SiO2 interface is
increased due to
quantum effects 
Negative shift of the
threshold voltage
G. Iannaccone
Potential [V]
Schrödinger + Drift-Diffusion
1.2
1.0
0.8
Poly Quantum
No Poly Quantum
-10 -8 -6 -4 -2
x [nm]
0
2
4
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
1
2
3
4
5
6
x [nm]
Università di Pisa
Series Resistance
Quantum Box
Co/Ti
Rdeep
Rext Rov
 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
200
Current [A/m]
Rcsd
Rcsd= contact resistance
Rdeep= HDD resistance
Rdeep= extension resistance
Rov= overlap resistance
150
Experiment
W=10nm
W=40nm
W=50nm
W=180nm
100 LG=40nm (T04)
50
0
0.00
0.25
0.50
VGS [V]
0.75
1.00
Università di Pisa
NanoTCAD2D
2D Poisson
+
1D Schrödinger
+
i) Ballistic Model (BM)
ii) Drift-diffusion per subband (DDS)
+
i)
ii)
1D Schrödinger
iii)
Quantum Bohm Potential (QBP)
2D Schrödinger
 The Schrödinger equation must be solved twice for each slice:
kz
 For the 2 minima along the vertical (kx) direction
2

2
 1 

~


x
,
y

 x m x li
  EC li  Eli  y li


l
k Tm
nli  B 2 t li

2
~

 Eli  E F
ln 1  exp 
k BT


ky



kx
 For the other 4 minima
2

2
kz
 1 

~


x
,
y


E


E
ti
C
ti
ti  y ti
 x m x



t
k T ml mt
nti  B
ti
2

G. Iannaccone
2
~

 Eti  E F
ln 1  exp 
k BT





ky
kx
Università di Pisa
Uniform stored charge in the dot layer
 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
z
y
dot
layer
x
gate
L
W
n+
SiO2
G. Iannaccone
Università di Pisa
Direct Tunneling Current
 The direct tunnel current is a
( E,electric
b )
function of Jthe
field (E)
and of the barrier heigth (Φb)
 The current density is larger
in correspondence of the
corner of the structure.
n   2nli   4nti
i
G. Iannaccone
i
Università di Pisa
Transfer characteristics from 3D simulation
 Effect of the stored charge on Vth shift
-4
100
10
Fresh Cell
19
-3
=3x10 cm
20
-3
=10 cm
-5
80
Current (A)
Current (A)
10
-6
10
-7
10
63 nm
-8
10
-9
60
40
20
20 nm
10
 Curvature radius 5nm
 Vth shift of about 0.5 V
and dependent on
-10
10
-1
0
1
2
3
4
Gate Voltage (V)
0
1
2
3
4
Assumption of locally
stored charge
proportional to the
local
Injected tunnel
current
Gate Voltage (V)
The transfer characteristics are not simply shifted
G. Iannaccone
Università di Pisa
Electron concentration at the Si-SiO2 interface
22
10
20
10
18
10
16
10
14
-3
10
Electron Concentration (cm )
-3
Electron Concentration(cm )
Programmed cell r=5 nm
63 nm
10
12
10
10
Vg=1.0 V
Vg=2.0 V
Vg=3.0 V
Vg=4.0 V
0
10
20
20 nm
30
40
50
60
Curvilinear Coordinate (nm)
70
22
10
20
10
18
10
16
10
14
10
12
10
10
10
8
10
6
10
4
10
2
10
0
10
-2
10
-4
10
-6
10
Vg=1.0 V
Fresh Cell
19
-3
=3x10 cm
20
-3
=10 cm
0
10
20
30
40
50
60
70
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).
G. Iannaccone
Università di Pisa