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Understanding Quasi Ballistic Transport in Si
and Alternative Channel Material MOSFETs
R. Clerc, Q. Rafhay, M. Ferrier, G. Pananakakis, G. Ghibaudo
IMEP-LAHC, INPG, Minatec, Grenoble, France
P. Palestri, L. Lucci, D. Esseni, L. Selmi
DIEGM, Univ. Udine, Italy
in collaboration with STMicroelectronics, Crolles : F. Bœuf and T. Skotnicki
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Introduction
Nano MOSFET (L < 20 nm) challenges our understanding of device physics
To attain adequate drive current for the highly scaled MOSFETs, quasi-ballistic operation
with enhanced thermal velocity and injection at the source end appears to be needed.
Eventually, nanowires, carbon nanotubes, or other high transport channel materials
(e.g., germanium or III-V thin channels on silicon) may be needed.
ITRS 2005
AIM of this presentation :
discuss the state of the art of the understanding of transport
in Quasi Ballistic Nano MOSFETs
SINANO project was the opportunity of a nice collaboration between :
IMEP Grenoble (Analytical Modeling)
and the University of Udine (Modeling and Simulation)
in the framework of the WP4 : Modelling and Simulation of nanodevices
Coordinator: Enrico Sangiorgi (Univ. Bologna)
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Outline
BASICS CONCEPTS OF QUASI BALLISTIC TRANSPORT
APPLICATION TO Si UTB MOSFETs
EXTENSION TO ALTERNATIVE CHANNEL MATERIALS
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BASICS CONCEPTS
OF QUASI BALLISTIC TRANSPORT
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Basics of Ballistic transport
Transport in long channel devices
Source
Flux of carrier
Energy
Gate
(In quasi equilibrium)
Drain
(In quasi equilibrium)
Scattering
TRANSPORT LIMITED
BY THE CHANNEL
Virtual Source
V
d
Channel
L
Long channel :
Id 
1
L
when L  0, Id  +  ?
• NO : (in Drift Diffusion model) velocity can not exceed saturation velocity vsat Ion  W Qi vsat
• Saturation velocity applies when L >>  (scattering required)
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Basics of Ballistic transport
Transport in Ballistic devices
Source
Energy
Gate
(In quasi equilibrium)
Flux of carrier
(In quasi equilibrium)
Drain
TRANSPORT LIMITED
BY THE SOURCE INJECTION
L independant
Virtual Source
V
d
Channel
L
Id BAL  W Qi vinj
Performance are no longer limited by transport along
the channel, but by injection at the source end
M. Lundstrom.; Z. Ren,
“Essential physics of carrier transport in nanoscale MOSFETs”, IEEE Trans. Elec. Dev., Volume 49, No 1, p 133 – 141, January 2002
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Concept of Ballistic Enhancement Factor
• Ballistic limit (L independent) :
Ballistic limit
Ion  W Qi vinj
Drain Current (a.u)
L independent
Ballistic enhancement factor
Drift Diffusion
including Vsat
τ
L
Vinj
• Ballistic Enhancement Factor :
L independent
BEF 
Mean Free
Path
1
10
100
Drift Diffusion
1/L
1000
Channel Length (nm)
vinj
vsat
• In Si, BEF close to 1.
10000
• Necessity to improve Vinj
M. Lundstrom.; Z. Ren,
“Essential physics of carrier transport in nanoscale MOSFETs”, IEEE Trans. Elec. Dev., Volume 49, No 1, p 133 – 141, January 2002
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Injection velocity in the Natori Model
Injection velocity (105 m/s)
Natori’s approximation :
• Charge at the entrance of the channel controlled by the gate
i.e ideal MOSFET with negligible DIBL.
2
MC simulation
Natori
tsi = 3 nm
Comparison
with MC simulations (L ~ 4 tsi)
tsi = 6 nm
1
0.0
0.2
0.4
0.6
0.8
Gate Voltage Vg (V)
K. Natori, “ Ballistic metal oxide semiconductor field effect transistor ” Journal of Applied Physics, vol. 76 p. 4879 - 4890 (1994).
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The role of Density of State (DOS) in Injection Velocity Enhancement
Injection velocity of one subband: Vinj  Vinj 0
i
i
2 F1 / 2 (u i )
 F0 (u i )
i
Vinj
0 
2kT
 mTi
ui 
One subband
Two subbands
5
 Vy  ( y  0) 
4
3
2
0.4
0.2
0
0.2
0.4

Injection Velocity (105 m/s)
0.3
Average kinetic energy (eV)
Injection Velocity (105 m/s)
5
1
E F  Ei
kT
 2 k // 2

2 m //
0.2
0.1
0.6
EF – E0 (eV)
• decrease mT
• increase EF - E0
• decrease the number of subband
k T
0
0.4
0.2
0
0.2
0.4
0.6
4
Vinj 0
3
Vinj
2
Vinj 1
1
0.4
EF – E0 (eV)
0.2
0
0.2
0.4
0.6
EF – E0 (eV)
Decrease the 2D
Density of States
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Quantum Capacitance and Density of State (DOS)
• DOS reduction leads to Quantum Capacitance reduction (Dark Space effect enhancement)
• Quantum Limit (= 1 fully degenerated subband)
Qi 
Injection velocity (105 m/s)
DG :
2 C oxC q
2 C ox  C q
(Vg  VT )
10
w. Q. Capa
EOT = 5 Å
Vdd = 0.8 V
w.o. Q. Capa
2 mt
π 2
Dark Space = 2.7 Å
M. De Michielis, D. Esseni, F. Driussi,
“Analytical Models for the Insight Into the Use of Alternative Channel Materials
in Ballistic nano-MOSFETs”
IEEE Trans. Elec. Dev., p. 155-122, January 2007
Quantum Limit
8
6
with
Cq  q 2
4
2
vth
0
0
0.2
0.4
0.6
0.8
1
Transverse Eff. Mass mt
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APPLICATION
TO Si UTB MOSFETs
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+15%
2.2
DG
SG
DG + strain
SG + strain
2.0
1.8
+ 40%
1.6
+7%
1.4
8
10 12 14 16 18 20 22 24 26
Channel length (nm)
Drain Current IDG/2 (103 µA/µm)
Injection velocity (105 m/s)
How to reduce DOS in Si MOSFET ?
Fully Ballistic
1.5
6
3
5
4
10
6
Quasi Ballistic r =0.4
t (nm) =
3 si
10 6 3
2
1.3
1.4
1.5
1.5
1.6
1.7
Injection Velocity
1.8
(105
1.9
m/s)
• by scaling body thickness ? Not efficient
• using biaxial strain (+ 40 %)
• no significant enhancement of quantum capacitance
M. Ferrier, R. Clerc, L. Lucci, Q. Rafhay, G. Pananakakis, G. Ghibaudo, F. Boeuf, T. Skotnicki.
« Conventional Technological Boosters for Injection Velocity in Ultra Thin Body MOSFETs »
accepted in IEEE Transaction On Nanotechnology
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Is Ballistic Transport Realistic ?
MC simulation reports that transport
in Si MOSFETs can not be considered
as Fully Ballistic
S. Eminente, D. Esseni, P. Palestri, C. Fiegna, L. Selmi, E. Sangiorgi
“ Understanding Quasi-Ballistic Transport in Nano-MOSFETs: Part II – Technology Scaling Along the ITRS”,
IEEE Transactions on Electron Devices, 52 p. 2736 - 2743 (2005).
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The role of scattering in Quasi Ballistic Devices
Introducting the concept of Back Scattering Coefficient r :
1  rHF vinj
BEF 

1  rHF vsat
Gate
F+
kT
Source
LkT
L
F-
Drain
rHF = Back Scattering Coefficient at High Field
rHF 
L kT
L kT  λ
empirical
intuited as a generalization of rLF
rLF 
0 
2 kT
µ
evth
L
L
M. Lundstrom Z. Ren, IEEE TED 49 p.133 (2002)
• theory of the High Field Backscattering coefficient has been re investigated in :
R. Clerc, P. Palestri, L. Selmi, IEEE TED 53, p 1634 – 1640 (2006)
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Validation by MC simulations
rHF 
L kT
L kT  λ
0 
??
rHF extracted is in fact
a function of LkT
2 kT
µ
evth
??
 extracted is in fact
proportional to µ
Extracted Dev (nm)
20
rMC 
L kT
L kT   Dev
0 
2 kT
µ
evth
DG 10 nm
10
Strained Bulk
Bulk
0
0
λ
λ 0
2
DG 4 nm
100
200
300
400
500
2
MC low field mobility (cm V-1s-1)
IEDM 2006
« Multi Subband Monte Carlo investigation of the mean free path and of the kT layer in degenerated quasi ballistic MOSFETs »
P. Palestri, R. Clerc, D. Esseni, L. Lucci, L. Selmi
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Strain Silicon : double advantage in QB devices
Injection Velocity 107cm/s
Analytical Model
2.5
2
1.5
1
0.5
0
Bulk
Ph. Acoustic
Ph. Optical
Surf. Roughness
Tsi Fluctuation
DG 12
0.5
Back Scattering r
D. Ponton et.al. Proc. Essderc 2006 p. 166
Multi Subband
Monte Carlo Simulations
0.4
r
L kT
L kT  

2 µeff (E eff ) kT/e
v th
0.3
0.2
0.1
0
Bulk DG 12
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Conclusion : Device Optimisation in the Quasi Ballistic Regime
3500
2 possible strategies to improve Ion :
Ion Current (µA/µm)
3000
Strained
Undoped UTB
• improving , which mean improving 
= effective field mobility
2500
Undoped UTB
Bulk
2000
like in pure Drift Diffusion model !
1500
DD
vsat=105 m/s
1000
• improving Vinj
(subband engineering)
by DOS reduction
500
0
1
10
100
1000
10000
Channel Length (nm)
BULK
µ = 130 cm2V-1s-1
Vinj = 1.2  105 m/s
Ninv = 1.451013 cm-2
Undoped UTB
µ = 200 cm2V-1s-1
Vinj = 1.2  105 m/s
Ninv = 1.451013 cm-2
Still no clear experimental evidence
Strained Undoped UTB
µ = 370 cm2V-1s-1
Vinj = 1.3  105 m/s
Ninv = 1.451013 cm-2
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EXTENSION
TO ALTERNATIVE CHANNEL MATERIALS
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Improving Quasi Ballistic Performance
by changing Channel Material
• improving , which mean improving 
• improving Vinj, by DOS reduction
Electrons
Bulk Mobility
at room temperature
Eff. Masses
Si
µ = 1500 cm2 V-1 s-1
ml = 0.98
mt = 0.19
Ge
µ = 3900 cm2 V-1 s-1
ml = 1.64
mt = 0.082
GaAs
µ = 8500 cm2 V-1 s-1
m = 0.067
However, it is not so easy !
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ISSUE 1 :
The role of quantum confinement
in the occupancy of subbands with light isotropic mass
1.0
G
0.8
0.6
L2'
0.4
0.2
L2
0.0
0
1
2
3
Injection velocity x 105 m/s
Relative occupancy
tGaAs=5nm, oriented 110
6
G
5
4
Global Vinj
3
L’2
2
L2
1
0
Gate voltage (V)
0.5
1
1.5
2
2.5
3
Gate Voltage (V)
ULIS 2007
« Further Investigations of the Impact of Channel Orientation on Ballistic Current of nDGFETs with Alternative Channel Materials »
Q. Rafhay, R. Clerc, M. Bescond, M. Ferrier, G. Ghibaudo
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ISSUE 2 :
Substrate orientation and channel direction
have to be re-optimized
Literature :
Current on (110) / Current on (100)
T. Low et al, IEDM 2003 : Ge best on (110)/[110]
A. Pethe et al, IEDM 2005 : Carriers in III-V moves from Γ to L
1,4
-2
13
Ninv = 10 cm
Ioff = 1nA/µm
1,3
InSb
1,2
(110)/[110] optimum direction of the
ballistic drain current for
Ge – GaAs – InAs and InSb DGFETs
Ge
InAs
1,1
GaAs
1,0
1
2
3
4
5
6
7
Semiconductor film thickness (nm)
ULIS 2007
« Further Investigations of the Impact of Channel Orientation on Ballistic Current of nDGFETs with Alternative Channel Materials »
Q. Rafhay, R. Clerc, M. Bescond, M. Ferrier, G. Ghibaudo
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ISSUE 3 : A good MATERIAL mobility does not necessary imply
a good DEVICE mobility
Example : MC Inversion layer electron mobility simulation of Ge 100
MATERIAL
7
1600
Velocity (cm/s)
-1
-1
Effective Mobility (cm².V.s )
10
DEVICE
10
6
100
Measurement [Jacoboni]
Bulk simulation
Mode Space Approach
1000
10000
Si  2.6
1200
800
Ge
400
Si
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Effective Field (MV/cm)
Lateral Field (V/cm)
SSDM 2007
« Mobility and Backscattering in Germanium n-type Inversion Layers »
Q. Rafhay, P. Palestri, D. Esseni, R. Clerc, L. Selmi
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Tentative Explanation :

-1
0.8
0.6
0.4
0.2

2400
Λ
-1
1.0
G
GAP
Effective Mobility (cm².V .s )
Relative valley occupancy
Q. Confinement enhances
Phonon Limited poor  mobility
Λ
Δ
0.0
0.3 0.6 0.9 1.2 1.5
2000
1600
1200
Δ
800
400
0.2
Effective field
0.4
0.6
0.8
1.0
1.2
1.4
Effective Field (MV/cm)
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ISSUE 4 :
Alternative Material may enhance leakages
Thermoionic Current
including SCE & DIBL
EFS
CB
VB
Source to Drain
Tunneling (SDT)
Band to Band
Tunneling (SDT)
EFD
A serious hindrance […] is the lack of an adequate quantitative model for interband
tunneling in indirect materials like Si and Ge. Most of the available expressions contain
adjustable parameters for the electron– phonon coupling constant […] . Their quantitative accuracy is open
to question […]
S. Luryi et al. SSE 51 p212 (2007)
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An simple model to illustrate the role of Source To Drain Tunneling
in Alternative Channel Materials
• We consider :
- Si like Material operating in the quantum limit
- 2 valleys with ml = 1 and mt varies from 0.01 to 1
mt
mt
• Ion is computed according the Natori Model in the quantum limit
(accounting for quantum capacitance)
• Potential Energy in weak inversion is computed according the Liu model
• Source to Drain Tunneling is computed using WKB transparency
(more accurate simulations including all subbands will be presented elsewhere)
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Leakages modeling versus Eff. Masses
Drain current (µA/µm)
Potential Energy (a.u)
5
Vg
L = 6 nm
tsi = 2 nm, EOT = 6 Å
0
0.2
0.4
0.6
0.8
1
104
103
10
100
10
1
0.1
0.01
3
10 4
10 5
10 6
10 7
10 8
10 9
1010
10 11
10 12
10 13
10 14
10 15
10 16
10 17
10 18
10
L = 6 nm
EOT = 5 Å
Vdd = 0.8 V
VT  0.2 V
mt
ideal slope
1
Normalized Distance (y/L)
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0.5
0
0.5
1
1.5
Gate Voltage (V)
26
Ion - Ioff Trade Off versus Eff. Masses
• Ioff kept constant at 0.11 µA/µm (tuning VFB)
22 nm node
Si
Si
L = 9 nm
EOT = 5 Å
Vdd = 0.8 V
L = 6 nm
EOT = 5 Å
Vdd = 0.8 V
Ion current (a.u)
Ion current (a.u.)
w.o. Q. Capa
16 nm node
w. Q. Capa
w.o. Q. Capa
w. Q. Capa
0
0.2
0.4
0.6
0.8
1
0
0.2
Transverse Eff. Mass mt
0.4
0.6
0.8
1
Transverse Eff. Mass mt
Si already offers a not so bad trade off after all !!
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Conclusions
Quasi Ballistic Transport may lead to an improvement of On state current in nano MOSFETs
(L  mfp )
1  rHF vinj
BEF 

1  rHF vsat
Strategies for performance enhancements :
improving long channel low field mobility
improving injection velocity by DOS reduction
using Strain Si
for instance
Alternative Channel materials have to face several challenges :
• Quantum Capacitance
Again Strain Si might offer
• Reduction of device mobility due to quantum confinement
the best trade off !!
• Leakages and especially Source to Drain Tunneling
Simulators have to improve to properly model leakage (BTBT, SDT)
Experimental validations are needed, especially on short channel device with Ultra Thin Body
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BACK UP SLIDES
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mt = 0.2
EOT = 6 Å
w.o Q. Capa
w Q. Capa
0.2
0.4
0.6
0.8
Gate Voltage (V)
1
EOT = 6 Å
Drain Current (a.u)
Drain Current (a.u)
Ion current in the quantum limit approximation
1.2
w.o Q. Capa
w Q. Capa
0
0.2
0.4
0.6
0.8
1
Transverse Eff. Mass mt
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Ballistic Ratio Iscat /Ibal
Undoped DG
tsi = 6 nm
EOT = 5 Å
0.9
0.7
universal
L independant µ
0.5
0.3
L dependant µ
Cros IEDM 2006
(neutral defects ?)
0.1
1
10
100
Channel length (nm)
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V( x )  kT
x
L kT
Average Velocity (105 m/s)
Backscattering Coef. r
1
 = 64 nm
 = 36
nm
0.1
MC
Improved r model
 = 18 nm
0.01
1
LkT/(LkT+)
10
kT layer length LkT (nm)
 = 18 nm LkT = 2 nm
4
Symbol : MC
Lines : model
V( x )  kT
x
L kT
LkT = 4 nm
3
LkT = 2 nm
2
 x
V( x )  kT 
 L kT



2
1
LkT = 4 nm
0
100
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4
8
12
Distance (nm)
16
20
32