Post on 20-May-2018
Hiroshi Iwai
Frontier Research CenterTokyo Institute of Technology
Futur of Nano CMOS TechnologyFutur of Nano CMOS Technology
January 3, 2014, At IBM SRDC (Semiconductor Research and Development Center). Bangalore
1
Back ground for nano-electronics
2
1900 “Electronics” started.
Device: Vacuum tubeDevice feature size: 10 cm
1970 “Micro-Electronics” started.
Device: Si MOS integrated circuitsDevice feature size: 10 µm
Major Appl.: Amplifier (Radio, TV, Wireless etc.)
Major Appl.: Digital (Computer, PC, etc.)
Technology Revolution
Technology Revolution
3
2000 “Nano-Electronics” started.
Device: Still, Si CMOS integrated circuitsDevice feature size: 100 nmMajor Appl.: Digital (µ-processor, cell phone, etc.)
Technology Revolution??
Maybe, just evolution or innovation!
But very important so many innovations!
4
Now, 2013 “Nano-Electronics” continued.
Device: Still, Si CMOS integrated circuitsDevice feature size: near 10 nmMajor Appl.: Still Digital (µ-processor, cell phone, etc.)
But, so many important emerging applications for smart society.
Still evolution and innovation..
5
Future, “Nano-Electronics” still continued?
Device: Still, Si CMOS integrated circuits?
Device feature size: ? nm, what is the limit?
Application: New application?
Any Technology Revolution?
Questions for future
6
What is special or new for Nano-Electronics?
In 1990’s, people expected completely new mechanism or operational principle due the nano size, like quantum mechanical effects.
However, no fancy new operational principle was found.
At least for logic application, there is no success story for “Beyond CMOS devices” to replace Si-CMOS.
Of course, I do not deny the importance of Beyond CMOStechnology development. It is becoming very importantas CMOS approach its limit.
7
1. Back ground for nano-CMOS
8
First Computer Eniac: made of huge number of vacuum tubes 1946Big size, huge power, short life time filament
Today's pocket PCmade of semiconductor
has much higher performance with
extremely low power consumption
dreamed of replacing vacuum tube with solid‐state device
9
1960: First MOSFET by D. Kahng and M. Atalla
Top View
Al Gate
Source
Drain
Si
Si
Al
SiO2
Si
Si/SiO2 Interface is extraordinarily good
10
1970,71: 1st generation of LSIs
DRAM Intel 1103 MPU Intel 4004
11
Most Recent SD Card
128GB (Bite) = 128G X 8bit= 1T(Tera)bit
1T = 1012 = 1Trillion
Brain Cell:10~100 BillionWorld Population:7 Billion
Stars in Galaxy:100 Billion
In 2012
12
2.4cm X 3.2cm X 0.21cm
Volume:1. 6cm³ Weight:2g
Voltage:2.7 - 3.6V
Old Vacuum Tube:5cm X 5cm X 10cm, 100g, 50W
128 GB = 1Tbit
What are volume, weight, power consumption for 1Tbit
13
Old Vacuum Tube:5cm X 5cm X 10cm
1Tbit = 10,000 X 10,000 X 10,000 bitVolume = (5cm X 10,000) X (5cm X 10,000)
X (10cm X 10,000)= 0.5km X 0.5km X 1km
500 m
1,000 m
1Tbit
Burji KhalifaDubai, UAE(Year 2010)
828 m
Indian TowerMumbai, India(Year 2016)
700 m
700 m
Pingan IntenationalFinance Center
Shanghai, China(Year 2016)
14
Old Vacuum Tube:50W
1Tbit = 1012bitPower = 0.05kWX1012=50 TW
Nuclear Power Generator1MkW=1BW We need 50,000 Nuclear Power Plant for
just one 128 GB memory
In Japan we have only 54 Nuclear Power Generator
Last summer Tokyo Electric Power Company (TEPCO) can
supply only 55BW.
We need 1000 TEPCO just one 128 GB memory
Imagine how many memories are used in the world! 15
So progress of integrated circuits is extremely
important for power saving
16
Brain: Integrated Circuits
Hands, Legs:Power device
Stomach:PV device
Ear, Eye:Sensor
Mouth:RF/Opto device
17
18
Near future smart-society has to treat huge data.
Demand to high-performance and low power CMOS become much more stronger.
19
Semiconductor Device Market will grow 5 times in 12 years, even
though, it is very matured market!!
Gartner: By K. Kim, CSTIC 2012
300B USD
2011
1,500B USD
2025
2. Current status of Si-CMOS device technologies
20
Downsizing
Thus, important forDecreasing cost, power
Increasing performance21
Decreasing sizeDecreasing capacitance
22
(1970) 10 μm 8 μm 6 μm 4 μm 3 μm 2 μm 1.2 μm
0.8 μm 0.5 μm 0.35 μm 0.25 μm 180 nm 130 nm
90 nm 65 nm 45 nm 32 nm (28 nm ) 22 nm(2012)
Feature Size / Technology Node
From 1970 to 2013 (Last year)
18 generationsLine width: 1/450
Area: 1/200,000
43 years 1 generation2.5 years
Line width: 1/1.43 = 0.70
Area: 1/2 = 0.5
What is the problem problem for downsizing?
Question
23
The problem for downsizing
Ioff increase: Transistor cannot be turned‐off.
Ioff (Off‐leakage current) between S and D
24
1. Punch‐through between S and D
2. Direct‐tunneling between S and D
3. Subthreshold current between S and D
S and D distance small
Ion & Ioff increase
25
1. Punch‐through between S and D
Gate oxide
Gate metal
Source Drain
1V0V0V
Substrate 0V DepletionRegion (DL)by Drain Bias
1V
0V 0V
tox and Vdd have to be decreased for better channel potential control IOFF Suppression
0V < Vdep<1V
0V
0V < Vdep<1VChannel
0V
0V
0V0V
0.5V
Large IOFF
Region governed By drain bias
Region governed by gate bias
tOX, Vdd thinning
DL touch with SRegion (DL)
Large IOFF
No tox. Vddthinning
Vdd
Vdd
26
Problem for downsizing
(Electron current)
27
1. Punch‐through between S and D
There are solutions to suppress the depletion layer
1.Decrease supply voltage Very difficult
2.Decrease tox to enhance the channel potential controllability by gate bias
as explained later
3. Gate/channel configuration change to enhance the channel potential controllability by gate bias
Fin‐FET, ET‐SOI, etc.
28
Decrease tox
Increase the Electric field between Gate &Channel
Increase the channel potential controllability by gate bias.
Suppress the depletion layer
Keep channel potential 0V
LLgate gate and tand toxox(EOT) scaling trend(EOT) scaling trendA. Toriumi (Tokyo Univ), IEDM 2006, Short Course
t ox(
(
29
30
Configuration change for channel and gate structures for better control of channel potential.
Fin‐FET, ET‐SOI, etc.
1V0V
0V
S
0V
0V <V<1V
1V0V
0V
0V
0VS D
G
G
G
Extremely Thin (or Fully-Depleted) SOI
Planar ET (or FD) SOI31
Si
SiO2
Extremely thin Si
Drain bias induced depletion
- Make Si layer thin- Control channel potential also from the bottom
1V0V
0V
S
0V
0V <V<1V
1V0V
0V
0V
0VS D
G
G
G
Surrounding gate structure (Multiple gates)
Planar Multi gate32
Si fin or nanowire
Drain bias induced depletion
- Make Si layer thin- Control channel potential also by multiple gates
not only from top & bottom but maybe also from side
Fin Tri-gate(Variation)
Ω-gate All-around
G G G
G
GNanowire structures in a wide meaning
33
G
Tri-gate
Our work at TIT: Our work at TIT: ΩΩ--gate Si Nanowiregate Si NanowireS. Sato et al., pp.361, ESSDERC2010 (Tokyo Tech.)
19 nm
12 nm
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
-1.5 -1.0 -0.5 0.0 0.5 1.010-12
Gate Voltage (V)
pFET nFET
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
Dra
in C
urre
nt (A
)
Vd=-50mV
Vd=-1V
Vd=50mV
Vd=1V
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
-1.5 -1.0 -0.5 0.0 0.5 1.010-12
Gate Voltage (V)
pFET nFET
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
Dra
in C
urre
nt (A
)
Vd=-50mV
Vd=-1V
Vd=50mV
Vd=1V
0 0.5 1 1.5 2ION (mA/µm)
Lg=65nm
0 0.5 1 1.5 2ION (mA/µm)
Lg=65nm
Lg=65nm
Poly-Si
SiO2
SiNSiN
SiO2
NW
・Conventional CMOS process
・High drive current
(1.32 mA/µm @ IOFF=117 nA/µm)
・DIBL of 62mV/V and SS of 70mV/dec for nFET 34
35
2. Direct‐tunneling between S and D
Wave function of electron penetrates the channel potential barriers by quantum mechanical physics, when the channel length is around 3 nm.
Tunnelingdistance
3 nm
Source DrainChannel
36
Ene
rgy
or P
oten
tial
for E
lect
ron
Direct‐tunnelcurrent
There is no solutions!
Downsizing limit is @ Lg = 3 nm.
37
3. Subthreshold current between S and D
38
Vg
Id
Vth (Threshold Voltage)
Vg=0V
SubthreshouldLeakage Current
Subtheshold leakage current of MOSFET
ONOFF
Ion
Subthresholdregion
39
Vg (V)1
0.3 V
0.5 V 1.0 V
Ion
Ioff
Id (A/µm)
10-7
10-5
10-11
10-9
Vd
Vth
0.15 V
0 0.5
Subthreshold leakage current
Electron EnergyBoltzmann statics
Exp (qV/kT)
Lg 1/2
Vd, Vg 1/2Vth 1/2
Ioff 103 in this exampleHowever
Because of log-linear dependence
40
Vg
Id
Vth (Threshold Voltage)
Vg=0V
SubthreshouldLeakage Current
Subtheshold leakage current of MOSFET
Subthreshold CurrentIs OK at Single Tr. level
But not OKFor Billions of Trs.
ONOFF
Ion
Subthresholdregion
41
3. Subthreshold current between S and D
Solution: however very difficult
Keep Vth as high as possible‐ Do not decrease supply voltage, Vd
‐ Suppress variability in VthHowever, punchthough enhanced
Thus, subthreshold current will limit the downsizing, especially for mobile devices
42Subthreshold Leakage (A/µm)
Ope
ratio
n Fr
eque
ncy
(a.u
.)
e)
100
10
1
Source: 2007 ITRS Winter Public Conf.
The limit is deferent depending on application
How far can we go for production?
10µm 8µm 6µm 4µm 3µm 2µm 1.2µm 0.8µm 0.5µm
0.35µm 0.25µm 180nm 130nm 90nm 65nm 45nm 32nm
(28nm) 22nm 14nm 11.5 nm 8nm 5.5nm? 4nm? 2.9 nm?
Past 0.7 times per 2.5 years
Now Future
・At least 4,5 generations to 8 ~ 5 nm
43
Intermediatenode
Direct-tunnelSubthresholdpunchthrough
Limit depending on applications
Fundamentallimit
However, careful about the name of technology!
22 nm Technology by Intel
Lg (Gate length) = 30 nm (HP), 34 nm (MP), 34 nm or larger (SP)
IEDM 2012, VLSI 2013
10 nm Technology by Leti (FD-SOI)
Lg (Gate length) = 15 nm
ECS 2013
Recently, Gate length (Lg) is much larger than the Technology name
The rate for the shrinkage for the gate length and line pitch will be larger than 0.7 in near future, because of the subthreshold leakage, and also because of the delay in EUV lithography.
As a result, we will have more technology generations until reaching the downsizing limit,and the time to reach the limit will be delayed.
HP MP SP
TOX,E (nm) 0.9 0.9 0.9
LGATE (nm) 30 34 34
IOFF (nA/um) 20-100 5-20 1-5
Tri-gate has been implemented since 22nm node, enabling further scaling
C. Auth et al., pp.131, VLSI2012 (Intel)
TriTri--gate implementation for transistors gate implementation for transistors
46
How far can we go for production?
47
Thus, we may go down to “5 nm”technology by choozing whatever gate length we want for the application.
More Moore to More More MooreMore Moore to More More Moore
65nm 45nm 32nm
Technology node
M. Bohr, pp.1, IEDM2011 (Intel)P. Packan, pp.659, IEDM2009 (Intel)C. Auth et al., pp.131, VLSI2012 (Intel)T. B. Hook, pp.115, IEDM2011 (IBM)S. Bangsaruntip et al., pp.297, IEDM2009 (IBM)
Lg 35nm Lg 30nm
(Fin,Tri, Nanowire)
22nm 15nm, 11nm, 8nm, 5nm, 3nm
Alternative (III-V/Ge) Channel FinFET
Emerging Devices
Tri-Gate
Now Future
Si channelSi
Others
(ETSOI)Planar
Si is still main stream for future !! ET: Extremely Thin28nm
HighHigh--k gate dielectricsk gate dielectrics
Continued research and development
SiO2 IL (Interfacial Layer) is used at Si interface to realize good mobility
Technology for direct contact of high-k and Si is necessary
Remote SiO2-IL scavengingHfO2 (IBM)
EOT=0.52 nm
Si
La-silicate
MG
Direct contact with La-silicate (Tokyo.Tech)
T. Ando, et al., p.423, IEDM2009, (IBM) T. Kawanago, et al., T-ED, vol. 59, no. 2, p. 269, 2012 (Tokyo Tech.)
K. Mistry, et al., p.247, IEDM 2007, (Intel)
TiN
HfO2
Si
SiO2
EOT=0.9nmHfO2/SiO2(IBM)
T.C. Chen, et al., p.8, VLSI 2009, (IBM)
Hf-based oxides
45nmEOT:1nm
32nmEOT:0.95nm
22nmEOT:0.9nm
15nm, 11nm, 8nm, 5nm, 3nm,
K. Kakushima, et al., p.8, IWDTF 2008, (Tokyo Tech.)
EOT=0.37nm EOT=0.40nm EOT=0.48nm
0.48 → 0.37nm Increase of Id at 30%49
How far can we go for production?
50
Now, Ion/Ioff ratio is typically 106.
However, it degrades significantly with decrease in Vsupply.
Rather than Ioff value, Ion/Ioff ratio is important.
[a] C. Auth et al., pp.131, VLSI2012 (Intel).[b] K. Mistry et al., pp.247, IEDM2007 (Intel).[c] H.-J. Cho et al., pp.350, IEDM2011 (Samsung).[d] S. Saitoh et al., pp.11, VLSI2012 (Toshiba).[e] S. Bangsaruntip et al., pp.297, IEDM2009 (IBM).
[f] T. Yamashita et al., pp.14, VLSI2011 (IBM).[g] A. Khakifirooz et al., pp.117, VLSI2012 (IBM).
IIONON and Iand IOFFOFF benchmarkbenchmark
[h] G. Bidal et al., pp.240, VLSI2009 (STMicroelectronics).[i] S. Sato et al., pp.361, ESSDERC2010 (Tokyo Tech.)[j] K. Cheng et al., pp.419, IEDM2012 (IBM)
1
10
100
1000
10000
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2ION [mA/µm]
I OFF
[nA
/µm
]NMOS
Intel [a]Bulk 32nmVDD=0.8V
Intel [a]Tri-Gate 22nmVDD=0.8V
Intel [b]Bulk 45nmVDD=1V
Toshiba [d]Tri-Gate NWVDD=1V
Samsung [c]Bulk 20nmVDD=0.9V
IBM [5]GAA NWVDD=1V
IBM [g]FinFET 25nmVDD=1V
IBM [g]ETSOIVDD=0.9V
IBM [g]ETSOIVDD=1V
STMicro. [h]GAA NWVDD=0.9V
STMicro. [h]GAA NWVDD=1.1V
Tokyo Tech. [i]Ω-gate NWVDD=1V
IBM [j]ETSOIVDD=0.9VIeff
1
10
100
1000
10000
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6ION [mA/µm]
I OFF
[nA
/µm
]
PMOSIntel [a]Bulk 32nmVDD=0.8V
Intel [a]Tri-Gate 22nmVDD=0.8V
Intel [b]Bulk 45nmVDD=1V
IBM [g]ETSOIVDD=1VSamsung [c]
Bulk 20nmVDD=0.9V
IBM [e]GAA NWVDD=1V
IBM [f]FinFET 25nmVDD=1V
IBM [g]ETSOIVDD=0.9V
STMicro. [h]GAA NWVDD=1.1V
IBM [j]ETSOIVDD=0.9VIeff
Nanowire/Tri gate MOSFETs have advantage not only suppressing Ioff, but also for increasing Ion over planer MOSFETs
52
1. Because of higher mobility due to lower vertical electric field
2. Because of higher carrier density at the round corner
53
0 .E + 0 0
1 .E + 1 9
2 .E + 1 9
3 .E + 1 9
4 .E + 1 9
5 .E + 1 9
6 .E + 1 9
0 2 4 6 8Distance from SiNW Surface (nm)
6543210
角の部分
平らな部分
電子濃度(x1019cm-3)Electron Density
Edge portion
Flat portion
54
SiNW Band structure calculation
Cross section of Si NW
[001] [011] [111]D=1.96nm D=1.94nm D=1.93nm
First principal calculation,
Si nanowire FET with 1D Transport[001] [011] [111]0.86 0.94 0.89
OrientationDiameter (nm)
[001] [011] [111]3.00 3.94 1.93
OrientationDiameter (nm)
ZG G GZ ZWave Number
ZG G GZ ZWave Number
Ener
gy (e
V)
0
-1
0
1
Ener
gy (e
V)
0
-1
0
1
(a)
(b)
Small mass with [011]
Large number of quantum channels
with [001]
10 nm diameter Si(100)NW( 2341 atoms)
20 nm diameter Si(100)NW ( 8941 atoms )
Atomic models of a Si quantum dot and Si nanowires
6.6 nm diameter SiQD( 8651 atoms)
2 6
26
( , , ) ( , , )n m nm
x y z C x m x y zxψ ψ
=−
∂≈ + ∆
∂ ∑
1( ) ( ) ( ) ( )
Mesh
m n m i n ii
d x y zψ ψ ψ ψ=
≈ ∆ ∆ ∆∑∫ r r r r r
Real-Space Finite-DifferenceSparse Matrix
FFT free (FFT is inevitable in the conventional plane-wave code)
Kohn-Sham eq. (finite-difference)
3D grid is divided by several regionsfor parallel computation.
Higher-order finite difference
Integration
MPI_ISEND, MPI_IRECV
MPI_ALLREDUCE
RSDFT – suitable for parallel first-principles calculation -
MPI ( Message Passing Interface ) library
)()()(ˆ)]([21 2 rrrr nnn
PPnlocs vv φεφρ =⎟
⎠⎞
⎜⎝⎛ ++∇−
CPU0
CPU8CPU7CPU6
CPU5CPU4CPU3
CPU2CPU1
Higher-order finite difference pseudopotential methodJ. R. Chelikowsky et al., Phys. Rev. B, (1994)
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
|Vnew-Vold|^2
50403020100iteration
onvergence behavior for Si10701H1996
e.g.) The system over 10,000 atoms → Si10701H1996(7.6 nm diameter Si dot)
Massively Parallel Computing
Computational Time (with 1024 nodes of PACS-CS)
6781 sec. × 60 iteration step = 113 hour
Based on the finite-difference pseudopotential method (J. R. Chelikowsky et al., PRB1994)
Highly tuned for massively parallel computers
Computations are done on a massively-parallel cluster PACS-CS at University of Tsukuba.
(Theoretical Peak Performance = 5.6GFLOPS/node)
with our recently developed code “RSDFT”
Iwata et al, J. Comp. Phys., to be published.Real-Space Density-Functional Theory code
(RSDFT)
Grid points = 3,402,059Bands = 22,432
1.0
0.9
0.8
0.7
0.6
0.5
(eV
)
-0.6
-0.4
-0.2
0.0
(eV
)
1.2
1.1
1.0
0.9
0.8
0.7
(eV
)
-0.8
-0.4
0.0
0.4
(eV
)
3.4
3.2
3.0
2.8
2.6
(eV
)
-1.5
-1.0
-0.5
0.0
0.5
(eV
)
1.0
0.8
0.6
0.4
0.2
0.0DO
S ( S
tate
s / e
V a
tom
)
-12 -10 -8 -6 -4 -2 0 2(eV)
1.0
0.8
0.6
0.4
0.2
0.0DO
S ( S
tate
s / e
V a
tom
)
-12 -10 -8 -6 -4 -2 0 2(eV)
1.0
0.8
0.6
0.4
0.2
0.0DO
S ( S
tate
s / e
V a
tom
)
-10 -8 -6 -4 -2 0 2 4 6(eV)
Structure and DOS of Si(100)NWs (D=1nm, 4nm, and 8nm)
D = 4 nmSi341H84(425 atoms)KS band gap = 0.81eV
D=4nm D=8nmD=1nm
D=8 nmSi1361H164 (1525 atoms)
KS band gap=0.61eV
D=1 nmSi21H20(41 atoms)
KS band gap=2.60eV
KS band gap of bulk (LDA) = 0.53eV
Band structure of 8-nm-diameter Si nanowire near the CBM
1.0
0.9
0.8
0.7
0.6
0.5
(eV
)
0.300.250.200.150.100.050.00
S band gap = 0.608 eV (@Γ)
kz
kx
ky
82 meV (96 meV)
kx
Each band is4-dgenerate. 23 meV (24 meV)
)()()(22 2
2
*
2
2
2
2
2
*
2
rr Φ−=Φ⎥⎦
⎤⎢⎣
⎡
∂∂
−⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
+∂∂
− CBMlt zmyxm
εεhh
Effective mass equation
The band structure can be understood thatelectrons near the CBM in the bulk Si are
Confined within a cylindrical geometry.
Si12822H1544(14,366 atoms)・10nm diameter、3.3nm height、(100)・Grid spacing:0.45Å (~14Ry)・# of grid points:4,718,592・# of bands:29,024
・Memory:1,022GB~2,044GB
Si12822H1544
Top View Side View
Si nano wire with surface roughness
SiNW Band compact model
Landauer Formalism for Ballistic FET
From xmax to xmin
[ ][ ]∑
⎭⎬⎫
⎩⎨⎧
−+−+
⎟⎟⎠
⎞⎜⎜⎝
⎛=
i BiD
BiSi
BD TkE
TkEgqTkGI
/)(exp1/)(exp1ln
0
00 µ
µ
µS
µD
xO xmax xmin
Qf
Qb
k
Energy
µSµD
E0
E1
E2min
E2max
qVD
E2min
Qf
Qb
0
5
10
15
20
25
30
35
40
0 0.1 0.2 0.3 0.4 0.5
Drain Bias (V)
Current (uA)
IV Characteristics of Ballistic SiNW FET
T=1KT=300K
Vg-Vt=1.0 V
0.7 V
0.3 V
0.05 V
Small temperature dependency35µA/wire for 4 quantum channels
Model of Carrier Scattering
ChannelOpticalPhonon
Initial ElasticZone
Optical PhononEmission Zone
ε~kBT
ε*
Source
TransmissionProbability : Ti
Elastic Backscatt.Elastic Backscatt.
+(Optical Phonon Emission)
x00x
V(x)
F(0)
G(0)
Linear Potential Approx. : Electric Field E
TransmissionProbability
to Drain
To Drain
0Drain fromInjection )0()0()0()(
=⎟⎟⎠
⎞−=
FGFT ε
Résumé of the Compact Model
.)( 0
G
bfStG C
qVV
+=
−−−
µµα
.
22
ln
2
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−+
++=
oxox
oxox
oxG
ttrttr
Cεπ
0 1 1 ( ( ))( ) ( ) ( )1 exp 1 exp 1 exp
f b i i ii i S i S i D
B B B
q dkQ Q g T k dkk k kk T k T k T
επ ε µ ε µ ε µ
∞
−∞ −∞
⎤⎡ ⎧ ⎫⎥⎢ ⎪ ⎪
⎪ ⎪ ⎥⎢+ = − −⎨ ⎬ ⎥⎢ ⎧ ⎫ ⎧ ⎫ ⎧ ⎫− − −⎪ ⎪+ + + ⎥⎢ ⎨ ⎬ ⎨ ⎬ ⎨ ⎬⎪ ⎪⎢ ⎥⎩ ⎭ ⎩ ⎭ ⎩ ⎭⎣ ⎩ ⎭ ⎦
∑ ∫ ∫
.ln
2
⎟⎠⎞
⎜⎝⎛ +
=
rtr
Cox
oxG
επDDS qV=− µµ
Unknowns are ID, (µS-µ0), (µD-µ0), (Qf+Qb)
[ ]( , ) ( , )i s D ii
qI g f f T dε µ ε µ επ
= −∑ ∫h
( )0
00 0 0 0 0
2( )
2 ln
D qET
qExB D D qE mD Bε
εε
=+⎛ ⎞+ + + ⎜ ⎟
⎝ ⎠
PlanarGate
GAA(Electrostatics requirement)
(Carrier distributionin Subbands)
I-VD Characteritics (RT)
Electric current 20~25 µANo satruration at Large VD
0
5
10
15
20
25
30
35
40
45
0 0.1 0.2 0.3 0.4 0.5 0.6
Drain Bias [V]
Current [uA]
VG-Vt=0.1V,Bal.
VG-Vt=0.1V,Qbal
VG-Vt=0.4V,Bal.
VG-Vt=0.4V,Qbal.
VG-Vt=0.7V,Bal.
VG-Vt=0.7V,Qbal.
VG-Vt=1.0V,Bal.
VG-Vt=1.0V,Qbal.
70
Size and Corner Effects on Electron Mobility of Rectangular Silicon Nanowire MOSFETs
71
Introduction
(L. Sekaric et al., Appl. Phys. Lett., 2009)
(J. Chen et al., IEDM, 2008)
To analysis deviation from facet-driven operation,We investigate size and corner effects in the rectangular Si NW MOSFETs
Experimental results showed a drastic mobility increase in width <
20 nm
Expectation in facet-driven operation
Width
Mob
ility
(100)
(110)
(100)
(100)
72
Simulation methods
Using the parabolic EMA, we self-consistently solved 2D Schrödinger and Poisson equations in equilibrium
Using the Kubo-Greenwood formula (low-field limit), we calculated phonon-scattering-limited mobility (R. Kotlyar et al., APL, 2004 / S. Jin et al., JAP,2007)
Subband structure, Eµ, and wave function, Ψµ,
[ ]∫∞
−=µ
µµµµ
µ ρτµE
B
dEEfEfEEvETkn
q )(1)()()()( 2
∑′
′′=µ
µµµηηµ
ρδρ
πτ i
lv
B FEugTkΞ
E ,,2Si
2
ac )()(
1h
∑′
′′′ ⎟⎠⎞
⎜⎝⎛ +
−±−
±=µ
µµµηηµ
ωωρ
ωρπ
τ 21
21
)(1)(1
)(2
)()(
1,,
Si
2
mh
h jj
jj
jv
jtj N
EfEf
FEggKD
E
where
∫∫ ′′ = dxdyyxΨyxΨF22
, ),(),( µµµµForm factor
Intrasubbandscattering rate
Intersubbandscattering rate
73
Materials
(100)
[100]
[100]/(100) Si NW
(100)
[110]
[110]/(100) Si NW
(110)
[110]
[110]/(110) Si NW
Wafer orientationWire direction
Rectangular Si NW MOSFETs with various orientations
To take into account arbitrary direction, effective mass tensor needs to be re-expressed in each coordinate system (M. Bescond et al., Nanotechnol.,
2007)
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=−
t
l
l
mm
mM
/1000/1000/1
1
Example effective mass tensor:Red valley of [100]/(100) Si NW
y zx[010]
[100]
[001]
Constant energy surface
tox = 1 nmnon-doped channelno interface statesNinv = 0.8 x 1013 /cm2
x
y
z
GateSiO2
Si NW
w
h
xyz
74
Result 1: Cross-sectional electron density
Electron density (/cm
3)
h=
10 n
mh
= 10
nm
w = 14 nm 6 nm 3 nm
h=
10 n
m
・ Corner and side electron distributions hardly depend on size when w > 6 nm
(110)
(100)(1
00)
(100)
(110
)(1
00)
(100)
[100]
[100]/(100) Si NW
(100)
[110]
[110]/(100) Si NW
(110)
[110]
[110]/(110) Si NW
75
0
200
400
600
800
0 2 4 6 8 10 12 14 16
Mob
ility
(cm
2 /V・s
)
Width (nm)
Result 2: Size-dependent mobility[100]/(100)
[110]/(100)
[110]/(110)
・ Mobility does not drastically change in width larger than 10 nm(we could not explain the drastic mobility increase in the experimental results)
h = 10 nm
Now, we discuss the corner effect based on specially resolved mobility analysis
・When w < 6 nm, mobility is drastically changed by the increase in form factor and change of electron structure
76
Spatially resolved mobility analysis
),(
),(),(
2
local yxn
nyxΨyx
∑= µ
µµµ µµ
・ Mobility for each subband, µµ, is spatially independent
・ Local mobility shows spatially different contribution of each subband
∑=µ
µµ nyxΨyxn2
),(),(
where
77
Mobility (cm
2/V・s)
h=
10 n
m
w = 14 nm 6 nm 5 nm 4 nm 3 nm
・We can distinguish orientation and corner effects based on the spatially resolved mobility analysis・ Corner mobility is always lower than the (100)-surface mobility.
(100)
(100
)(1
00)
(100)
(110
)
(110)
h=
10 n
mh
= 10
nm
Result 3: Cross-sectional spatially resolved mobility
(100)[10
0]
[100]/(100) Si NW
(100)
[110]
[110]/(100) Si NW
(110)
[110]
[110]/(110) Si NW
78
02
46
810
12
02
46
810
12500
600
700
800
x (nm)y (nm)
Local mobility, µlocal(x,y) (cm2/V⋅ s)
Corner Side
Discussion 1: Corner effectElectron density Local mobility
Corner mobility is lower than side mobility
Velocity & scattering rate
he large ratio of corner electrons belongs to the 2nd Subband, which shows lower velocity and higher scattering rate
Subband occupancy ratio
02
46
810
12
02
46
810
120
2
4
6
8
10
x 1019
x (nm)y (nm)
Electron density, n(x,y) (/cm3)
Corner
Side
0
0.2
0.4
0.6
0.8
1
Num
ber o
f ele
ctro
ns (/
cm3 )
Corner Side
x 1020
Others
1st subband group
2nd subband group
-0.04 -0.02 0 0.02 0.040
1
2
3
4x 10
7
E - Efn (eV)
Group velocity, vµ (cm/s) (b)
1st
2nd
-0.04 -0.02 0 0.02 0.040
1
2
3
4
5x 10
13
E - Efn (eV)
Scattering rate, 1/τ µ (/s) (c)
1st 2nd
79
Discussion 2: Origin of different contribution between subbands
The large ratio of corner electrons belongs to the 2nd
Subband group
0
0.2
0.4
0.6
0.8
1
Num
ber o
f ele
ctro
ns (/
cm3 )
Corner Side
x 1020
Others
1st subband group
2nd subband group
Subband occupancy ratio
02
46
810
12
02
46
810
120
0.5
1
1.5
2
x 1013
x (nm)y (nm)
Probability density (/cm2)
02
46
810
12
02
46
810
120
0.5
1
1.5
2
x 1013
x (nm)y (nm)
Probability density (/cm2)
(b) 2nd subband group
(a) 1st subband group
Probability density
Probability density of the 2nd subband group with high energy is localized at
cornerbecause wave function within rapidly varying potential at corner could be
represented by high energy plane wave function basis
80
Velocity and Form Factor
・ Velocity increases with occupancy of the ground subband with small effective mass・ Scattering rate increases with increasing form factor
Trade-off in width dependence
0
200
400
600
800
0 2 4 6 8 10 12 14 16
Mob
ility
(cm
2 /V・s
)
Width (nm)
[100]/(100)
[110]/(100)
[110]/(110)
h = 10 nm
0.6
1.0
1.4
1.8
2.2
0 2 4 6 8 10 12 14 16Width (nm)
[100]/(100)
h = 10 nm
Velo
city
(cm
2 /V・s
)
0
20
40
60
0 2 4 6 8 10 12 14 16Width (nm)
[100]/(100)
h = 10 nmSca
tterin
g ra
te (s
-1)
81
We investigated the size-dependent phonon-scattering-limited mobility of rectangular Si NW MOSFETs
The drastic increase in mobility from experimental results could not be explained by size and corner effects (strain could cause the drastic
increase in mobility)
When w < 6 nm, the mobility drastically modulated
According to the specially resolved mobility analysis, the corner mobility was lower than the side mobility
Paper with respect to a part of thisY. Lee, K. Kakushima, K. Natori, and H. Iwai, “Corner effects on phonon-limited mobility in
rectangular silicon nanowire metal-oxide-semiconductor field-effect transistors based on spatially resolved mobility analysis,” J. Appl. Phys., Vol. 109, Issue 11, pp. 113712-1–113712-5, June 2011.
82
Modeling of Quasi-Ballistic Transport in Nanowire MOFSETs
A part of this work has been conducted with group of Prof. Giorgio Baccarani at University of Bologna
83
Quasi-ballistic transport
M. Lundstrom (EDL, 1997) modeled the quasi-ballistic transport with the kT layer
E. Gnani et al. (TED, 2008) and K. Natori (JJAP, 2009) modeled the quasi-ballistic transport with only elastic scattering
K. Natori (JJAP, 2009 / TED, 2011) modeled the quasi-ballistic transport both welastic and inelastic scatterings
kT0
kT
LLR+
=λ
R: Backscattering coefficientλ0: Mean free pathLkT: kT-layer length
K. Natori (JAP, 1994) modeled the ballistic MOSFET operation
(However, the scattering theory with kT layer has not been clearly postulated)
We develop a comprehensive model of the quasi-ballistic transport based on Natori’s model
As the MOSFET is extremely downscaled, diffusive transport changes to quasi-ballistic transport
84
Natori’s model for quasi-ballistic transport
Dividing the channel into two zones: elastic zone and relaxation zone
Elastic zone
Relaxation zone
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−
+
−
+
)0()0(
121
11
)()(
1
11
1e
e
ff
RRR
Rzfzf
Scattering matrix
where (from BTE)
ħωε
0z
ze
),(),()(1
),(),()](21[)(
),0(),0()(
e
e1
e
e11
εε
ε
εε
εε
εεε
zfzfR
zfzfRR
ffR
+
−
+
−
+
−
−
−+==
∫
∫+
=e
e
0ac
0ac
1
),(11
),(1
)(z
z
dzz
dzzR
ελ
ελε
2
ac
op
ac
op
e
e 1),(),(
⎟⎟⎠
⎞⎜⎜⎝
⎛−+≈+
−
SS
SS
zfzf
εε
(endless drain)
85
Concept of this studyDividing the device into five zones:source zone, barrier zone, elastic zone, relaxation zone, drain zone
ħωε
0 z0 ze zr zd
Idea
l dra
in
Idea
l sou
rce
Source zone
Drain zone
Elastic zone
Relaxation zone
Barrier zone
zs
・ Adopted elastic scattering is intravalley acoustic phonon (AP) scattering・ Si NW MOSFET is adopted to consider 1D transport
・ Adopted inelastic scattering is g3- and f3-type optical phonon (OP) scattering・ OP energies are set to 63 meV
86
One-flux scattering matrix
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−−
=⎟⎟⎠
⎞⎜⎜⎝
⎛−
+
−
+
)()(
11
)()(
1
1
1
22121
22
2
zfzf
RRRRTT
Tzfzf
f+(z1)R1
T1
T2
R2
z1 z2
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛−
+
−
+
)()(
)()(
2
1
21
21
1
2
zfzf
TRRT
zfzf
f–(z2)
f+(z2)f–(z1)
87
Expression with one-flux scattering matrices∫ −+ −= εεε
πdzfzfqI )],(),([ 00
h
Flux between z0 and zd
)(1))(()()1(
2121111211
2121212121211121
rrrrdedrre
rrrreeeeeeeerdre
RRTTRRRRRRRRTTRRTTRRTTRRRRR
−−−−−−+−+−
≡
)(1 2121111211
222
rrrrdedrre
dre
RRTTRRRRRRTTTT
−−−−≡
where
Flux between 0 and z0
Simultaneously solving them, f+(z0) and f-(z0) are described by Rs, Ts, fS, and fD
Solving BTE for each zone, we can derive Rs and Ts
ħωε
0 z0 ze zr zd
Idea
l dra
in
Idea
l sou
rce
Source zone
Drain zone
Elastic zone
Relaxation zone
Barrier zone
zs
12
212122
1)(
bs
bbbbsbS RR
RRTTRRR
−−−
≡
12
11
1 bs
bsS RR
TTT
−≡
DS
SS
S fRR
TfRRRT
zf−
+−
=−
11)( 0)()( 00 zfRfTzf SSS
−+ +=
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−−
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
=⎟⎟⎠
⎞⎜⎜⎝
⎛−−
+
)0(111
)()( S
1s
2s2s1s2s1s
1b
2b2b1b2b1b
2b2s0
0
ff
RRRRTT
RRRRTT
TTzfzf
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−−
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
=⎟⎟⎠
⎞⎜⎜⎝
⎛−
++
)()(
1111)z(
0
0
1e
2e2e1e2e1e
1r
2r2r1r2r1r
d1
d2d2d1d2d1
d2r2e2D
d
zfzf
RRRRTT
RRRRTT
RRRRTT
TTTff
88
ħωε
0 z0 ze zr zd
Idea
l dra
in
Idea
l sou
rce
Source zone
Drain zone
Elastic zone
Relaxation zone
Barrier zone
zs
Rb1,2 and Tb1,2 for barrier zone
BTE
where AP scattering only
If potential is given, we can calculate R and T
),(),(
1),(),(
1),( εελ
εελ
ε zfz
zfzdz
zdf
acac
−++
−=−
),(),(
1),(),(
1),( εελ
εελ
ε zfz
zfzdz
zdf
acac
+−−
−=
∫
∫
+==
0
0
),(11
),(1
)()( 21 z
zac
z
zac
bb
s
s
dzz
dzz
RR
ελ
ελεε
)(1)()( 121 εεε bbb RTT −==
Barrier zone is substantially short
)]()([4),(),(21
),(1
101 zEzEmS
zzvzac
acac −+=≡
επετεελ h
89
ħωε
0 z0 ze zr zd
Idea
l dra
in
Idea
l sou
rce
Source zone
Drain zone
Elastic zone
Relaxation zone
Barrier zone
zs
Re1,2 and Te1,2 for elastic zone
BTE
where AP scattering only
If potential is given, we can calculate R and T
),(),(
1),(),(
1),( εελ
εελ
ε zfz
zfzdz
zdf
acac
−++
−=−
),(),(
1),(),(
1),( εελ
εελ
ε zfz
zfzdz
zdf
acac
+−−
−=
∫
∫
+==
e
e
z
zac
z
zac
ee
dzz
dzz
RR
0
0
),(11
),(1
)()( 21
ελ
ελεε
)(1)()( 121 εεε eee RTT −==
)]()([4),(),(21
),(1
101 zEzEmS
zzvzac
acac −+=≡
επετεελ h
90
Validation of the approximation in elastic zone
Scattering rate under equilibrium (d = 3 nm, nondegenerate)
・ OP scattering can be neglected below the 63 meV
0 0.05 0.1 0.150
5
10
15x 10
13
ε (eV)
Sca
tterin
g ra
te (1
/s)
AP only
AP + OP
91
Rr1,2 and Tr1,2 for relaxation zone (1)
BTE
where AP + OP (emission only)
We approximate U(z0) + ε – U(z) >> ħω, to analytically solve BTE
To avoid excessive relaxation in degenerate system
)(),( ωεωε hh −≈−+Dfzf
)(),( ωεωε hh −≈−−Dfzf
ħωε
0 z0 ze zr zd
Idea
l dra
in
Idea
l sou
rce
Source zone
Drain zone
Elastic zone
Relaxation zone
Barrier zone
zs
),(),(
2/)],(),([1),(),(
1),(),(
1),( εελ
ωεωεεελ
εελ
ε zfz
zfzfzfz
zfzdz
zdf
opacac
+−+
−++ −+−−
+−=−hh
),(),(
2/)],(),([1),(),(
1),(),(
1),( εελ
ωεωεεελ
εελ
ε zfz
zfzfzfz
zfzdz
zdf
opacac
−−+
+−− −+−−
+−=hh
)]()([(2])()()][()([2),(),(1
),(1
101101101 zEzEmS
zEzEzEzEmS
zzvzopop
opop −+≈
−−+−+=≡
επωεεπετεελ hhh
)]()([4),(),(21
),(1
101 zEzEmS
zzvzac
acac −+=≡
επετεελ h
92
Rr1,2 and Tr1,2 for relaxation zone (2)
where
If potential is given, we can calculate R and T
⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟⎟
⎠
⎞⎜⎜⎝
⎛−+−⎟⎟
⎠
⎞⎜⎜⎝
⎛++
⎟⎟⎠
⎞⎜⎜⎝
⎛+−−
==
∫
∫g
e
g
e
z
zac
z
zac
rr
dzz
XXXXXX
dzz
XXRR
),(122exp
221
221
),(122exp1
)()(2
22
2
21
ελ
ελεε
⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟⎟
⎠
⎞⎜⎜⎝
⎛−+−⎟⎟
⎠
⎞⎜⎜⎝
⎛++
⎟⎟⎠
⎞⎜⎜⎝
⎛+−−+
==
∫
∫g
e
g
e
z
zac
z
zac
rr
dzz
XXXXXX
dzz
XXXXTT
),(122exp
221
221
),(122exp22
)()(2
22
22
21
ελ
ελεε
)](1[ ωε h−−≡ Dac
op fSS
X
93
Rs2,d2 and Ts1,d1 for source and drain zones (1)
BTE
Where (for source zone)
AP + OP (both in- and out-scattering)
Constant potential
To avoid excessive relaxation in the degenerate system
)(),( ωεωε hh −≈−+Sfzf
)(),( ωεωε hh −≈−−Sfzf
ħωε
0 z0 ze zr zd
Idea
l dra
in
Idea
l sou
rce
Source zone
Drain zone
Elastic zone
Relaxation zone
Barrier zone
zs
)],(1[/),(
2/)],(),([),(),(
2/)],(),([1),(),(
1),(),(
1),( εελ
ωεωεεελ
ωεωεεελ
εελ
ε zfSSz
zfzfzfz
zfzfzfz
zfzdz
zdf
opopopopacac
+−+
+−+
−++
−′−+−
−−+−−
+−=−hhhh
)],(1[/),(
2/)],(),([),(),(
2/)],(),([1),(),(
1),(),(
1),( εελ
ωεωεεελ
ωεωεεελ
εελ
ε zfSSz
zfzfzfz
zfzfzfz
zfzdz
zdf
opopopopacac
−−+
−−+
+−−
−′−+−
−−+−−
+−=hhhh
)](1)[(),()](1)[(),( εωεεωεεε SSopSSop ffzSffzS −−=−−′hh
Detailed balance conditionTo apply appropriate in-scattering rate
])([4)(1
),(1
s101
acsacac EzE
mSz −+
≡≈επελελ h
])(][)([2)(1
),(1
s101
s101
opsopop ωεεπελελ hh −−+−+
≡≈EzEEzE
mSz
94
Modified BTE
where
where
We can calculate R and T from length of source and drain
Rs2,d2 and Ts1,d1 for source and drain zones (2)
)(1),(
)(1),(
)(1
)(1),(
ελε
ελε
ελελε
sin
sac
sout
sac
zfzfdzzdf
−−⎟⎟⎠
⎞⎜⎜⎝
⎛+=− −+
+
)(1),(
)(1),(
)(1
)(1),(
ελε
ελε
ελελε
sin
sac
sout
sac
zfzfdzzdf
−−⎟⎟⎠
⎞⎜⎜⎝
⎛+= +−
− )](1)[()(1
)(1
Ssop
Ssout εελ
ωεελ f
f−−−
≡h
)](1)[()()](1[
)(1
Ssop
SSsin εελ
εωεελ f
ff−
−−≡
h
( )
( )ss
sout
s
sout
s
sout
s
sout
s
sss
LYY
Y
Y
Y
LYR
)(2exp
)(1)(
)(1)(
)(1)(
)(1)(
)(2exp1)(2
ε
ελε
ελε
ελε
ελε
εε
−+
−−
−
+
−−=
)(1)( 21 εε ss RT −=
where
Drain zone
( )
( )dd
dout
d
dout
d
dout
d
dout
d
ddd
LYY
Y
Y
Y
LYR
)(2exp
)(1)(
)(1)(
)(1)(
)(1)(
)(2exp1)(1
ε
ελε
ελε
ελε
ελε
εε
−+
−−
−
+
−−=
)(1)( 12 εε dd RT −=2d
outdout
dac )]([
1)()(
2)(ελελελ
ε +≡dY
2sout
sout
sac )]([
1)()(
2)(ελελελ
ε +≡sY
Source zone
With the same process
95
Summary of derived Rs and Ts
where
where
Elastic zone
Relaxation zone
Barrier zone
Source zone
∫
∫
+==
0
0
),(11
),(1
)()( 21 z
zac
z
zac
bb
s
s
dzz
dzz
RR
ελ
ελεε
)(1)()( 121 εεε bbb RTT −==
∫
∫
+==
e
e
z
zac
z
zac
ee
dzz
dzz
RR
0
0
),(11
),(1
)()( 21
ελ
ελεε
)(1)()( 121 εεε eee RTT −==
⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟⎟
⎠
⎞⎜⎜⎝
⎛−+−⎟⎟
⎠
⎞⎜⎜⎝
⎛++
⎟⎟⎠
⎞⎜⎜⎝
⎛+−−
==
∫
∫r
e
r
e
z
zac
z
zac
rr
dzz
XXXXXX
dzz
XXRR
),(122exp
221
221
),(122exp1
)()(2
22
2
21
ελ
ελεε
⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟⎟
⎠
⎞⎜⎜⎝
⎛−+−⎟⎟
⎠
⎞⎜⎜⎝
⎛++
⎟⎟⎠
⎞⎜⎜⎝
⎛+−−+
==
∫
∫r
e
r
e
z
zac
z
zac
rr
dzz
XXXXXX
dzz
XXXXTT
),(122exp
221
221
),(122exp22
)()(2
22
22
21
ελ
ελεε
)](1[ ωε h−−≡ Dac
op fSS
X
( )
( )ss
sout
s
sout
s
sout
s
sout
s
sss
LYY
Y
Y
Y
LYR
)(2exp
)(1)(
)(1)(
)(1)(
)(1)(
)(2exp1)(2
ε
ελε
ελε
ελε
ελε
εε
−+
−−
−
+
−−=
)(1)( 21 εε ss RT −=
2sout
sout
sac )]([
1)()(
2)(ελελελ
ε +≡sY
whereDrain zone ( )
( )dd
dout
d
dout
d
dout
d
dout
d
ddd
LYY
Y
Y
Y
LYR
)(2exp
)(1)(
)(1)(
)(1)(
)(1)(
)(2exp1)(1
ε
ελε
ελε
ελε
ελε
εε
−+
−−
−
+
−−=
)(1)( 12 εε dd RT −=
2dout
dout
dac )]([
1)()(
2)(ελελελ
ε +≡dY
)](1)[()(1
)(1
Ssop
Ssout εελ
ωεελ f
f−−−
≡h
)]()([4),(1
0 zUzUmS
zac
ac −+≡
επελ h
where
)](1)[()(1
)(1
Ddop
Ddout εελ
ωεελ f
f−−−
≡h
])([4)(1
d101
acdac EzE
mS−+
≡επελ h
])(][)([2)(1
d101
d101
opdop ωεεπελ hh −−+−+
≡EzEEzE
mS
])(][)([2)(1
s101
s101
opsop ωεεπελ hh −−+−+
≡EzEEzE
mS
])([4)(1
s101
acsac EzE
mS−+
≡επελ h
96
-0.4-0.35-0.3
-0.25-0.2
-0.15-0.1
-0.050
0 10 20 30 40 50
Validation by a numerical simulation
Importing self-consistent potential, Rs and Ts are semi-analytically calculated in our model
Position (nm)
Ene
rgy
(eV
)d=3nm (1D-like transport)Ls=10nmLg=30nmLd=10nmVg–Vt=0.3VVd=0.3V
We compare the results from our model and the numerical simulation based on the deterministic solution of 1D MSBTE
Example of self-consistently calculated potential profile
E1(z)
97
Numerical simulation based on the deterministic solution of 1D MSBTE
Longitudinal BTE: fµ
Charge calculation: n
Poisson eq.: U
Convergence check
U0
Transverse Schrödinger eq.: Eµ, Rµ
rz
Deterministic solution of 1D MSBTE is more efficient than1D MSMC in the low
dimensionality of the nanowire
Results are the same as those from 1D MSMC
Cylindrical coordinate system
98
Validation 1: Backscattering coefficient
AP only
This model
・ This model is in good agreement with the numerical simulation especially below 63 meV
Numerical simulation
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2ε (eV)
R
Saturation regionVg – Vt = 0.3 V
Vd = 0.3 V
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2ε (eV)
R
Subthreshold regionVg – Vt = 0.0 V
Vd = 0.3 V
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2ε (eV)
R
Saturation region and long drainLd = 100 nm
Vg – Vt = 0.3 VVd = 0.3 V
・ Modeling for drain zone is available even in substantially long drain
99
Validation 2: Carrier distribution function at z0
・ Distribution function at the top of the barrier taken into account
・ Modeling of source zone is available even in substantially long source
0
0.2
0.4
0.6
0.8
1
0 0.1 0.20
0.2
0.4
0.6
0.8
1
00.10.2ε (eV)
Dis
tribu
tion
func
tion Solid lines: This model
Symbols: Numerical simulation
f+(z0,ε)f–(z0,ε)
Dotted line: fS(ε)
0
0.02
0.04
0.06
0.08
0.1
00.10.2ε (eV)
Dis
tribu
tion
func
tion
0
0.02
0.04
0.06
0.08
0.1
0 0.1 0.2
f+(z0,ε)f–(z0,ε)
Solid lines: This modelSymbols: Numerical simulation
Dotted line: fS(ε)
Long sourceLs = 100 nmVg – Vt = 0.0 VVd = 0.3 V
Saturation regionLs = 10 nmVg – Vt = 0.3 VVd = 0.3 V
100
Validation 3: I-V characteristics
・ This model is in quantitatively good agreement with the numerical simulation
012345678
0 0.1 0.2 0.3 0.4 0.5
V g– V t
= 0.3
V
Vg – Vt = 0.0 V
Drain voltage (V)
Dra
in c
urre
nt (µ
A)
Numerical simulation
This model
101
Linear potential
Lg LdLs
z
E
Source
Drain
Channel
0
Us
Ud
z0 zr zd
U(z0)
Discussion 1: Potential profile to investigate quasi-ballistic transport
・ R(ε) can be analytically derived
・ Us and Ud are self-consistently calculated with donor impurity density
・ To calculate drain current, we need numerical integration over energy
102
0
0.2
0.4
0.6
0.8
1
0 50 100 150Gate length (nm)
Bal
listic
ity
d = 3 nmLs = 10 nmLd = 1 nmVd = 0.3 VU(z0) = Efs
0
0.2
0.4
0.6
0.8
1
0 50 100 150Drain length (nm)
Bal
listic
ity
d = 3 nmLs = 10 nmLg = 1 nmVd = 0.3 VU(z0) = Efs
Discussion 2: Ballisticity
Ballisticity vs. Lg Ballisticity vs. Ld
・When Ld > 50 nm, 20 % is backscattered from drain zone
・ Considering realistic 1D drain, we can not obtain ‘ballisticity = 1’
・When Lg = 10 nm, 20 % is backscattered
103
0
1
2
3
4
5
0 50 100 150Source length (nm)
Dra
in c
urre
nt (µ
A)
d = 3 nmLg = 10 nmLd = 10 nmVd = 0.3 VU(z0) = Efs
This modelAP only
0
1
2
3
4
5
0 50 100 150Source length (nm)
Dra
in c
urre
nt (µ
A)
d = 3 nmLg = 10 nmLd = 10 nmVd = 0.3 VU(z0) = Efs
This modelAP only
Discussion 3: Source length dependence
・When Ls < 10 nm, elastic source approximation is available
・ In a shorter 1D source, the resistivity seems to be smaller
104
0
1
2
3
4
5
0 20 40 60Gate length (nm)
d = 3 nmLs = 10 nmLd = 10 nmVd = 0.3 VU(z0) = Efs
This modelNatori’s model
AP only
Dra
in c
urre
nt (µ
A)
Discussion 4: Comparison with other models (1)
・ In Lg > 50 nm, Natori’s model is in good agreement with this model
・ In Lg < 10 nm, elastic approximation is in good agreement with this model
Drain current vs. gate length
105
Discussion 5: Comparison with other models (2)
・ Elastic approximation could not describe backscattering in long drain
・ In Lg > 100 nm, Natori’s model is in good agreement with this model
00.5
11.5
22.5
33.5
44.5
0 50 100 150Drain length (nm)
Dra
in c
urre
nt (µ
A)
d = 3 nmLs = 10 nmLg = 10 nmVd = 0.3 VU(z0) = Efs
This modelNatori’s modelAP only
Drain current vs. drain length
106
Advantages of this model
ħωε
0 z0 ze zr zd
Idea
l dra
in
Idea
l sou
rce
Source zone
Drain zone
Elastic zone
Relaxation zone
Barrier zone
zs
・ Describing distribution function of the carrier injected from realistic source
・ Describing transmission coefficient for the carriers injected from drain
・ Taking into account finite length of drain and source as well aschannel
107
- Device is divided into five zones
・We have successfully modeled the quasi-ballistic transport in nanowire MOSF
- Backscattering coefficient, distribution function, and drain current were derived with one-flux scattering matrix and BTEs
・ Results from this model were in good agreement with those from anumerical simulation
・ 1D drain length was important to adjust backscattering coefficient
・ 1D source length was also important to represent distribution of the carriers injected from realistic source
108
Conclusions
- We successfully modeled the gate capacitance to distinguish different contributions of the quantum effects- The decrease in xavg caused the positive effect on the total capacitance
- We showed the effects of the size-dependent properties on performance- Desirable diameter could be around 5 nm
- We can suppress effective mass fluctuation by adopting square cross section
- We successfully developed the quasi-ballistic transport model of NW MOSFETs- Ls and Ld were also important to estimate the drain current
- Size and corner effects without strain could not cause the drastic mobility increase from experimental results- In width < 6 nm, mobility drastically modulated
By modeling gate capacitance and quasi-ballistic transport,we could interpret device physics
By numerical simulation, we investigatedwhat parameter control performance in ultra-scaled NW MOSFETs
SiNW FET Fabrication
Sacrificial Oxidation
SiN sidewall support formation
Ni SALISIDE Process (Ni 9nm / TiN 10nm)
S/D & Fin Patterning
Gate Oxidation & Poly-Si DepositionGate Lithography & RIE EtchingGate Sidewall Formation
30nm
30nm
30nm
Oixde etch back
Standard recipe for gate stack formationBackend
(a) SEM image of Si NW FET (Lg = 200nm) (b) high magnification observation of gate and its sidewall.
110
Fabricated SiNW FET
30nm
Poly-Si
SiN
Nanow
ire
SiN support
SiNW
Lg=65nm, Tox=3nm
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
-1.5 -1.0 -0.5 0.0 0.5 1.0
0.E+00
1.E-05
2.E-05
3.E-05
4.E-05
5.E-05
6.E-05
7.E-05
-1.0 -0.5 0.0 0.5 1.00
10 20 30 40 50 60 70
Dra
in C
urre
nt (µ
A)
Drain Voltage (V)
Vg-Vth=1.0 V
Vg-Vth= -1.0 V
0.8 V
0.6 V
0.4 V
0.2 V
(a)
10-12
Gate Voltage (V)
pFET nFET
(b)
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
Dra
in C
urre
nt (A
)
Vd=-50mV
Vd=-1V
Vd=50mV
Vd=1V
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
-1.5 -1.0 -0.5 0.0 0.5 1.0
0.E+00
1.E-05
2.E-05
3.E-05
4.E-05
5.E-05
6.E-05
7.E-05
-1.0 -0.5 0.0 0.5 1.00
10 20 30 40 50 60 70
Dra
in C
urre
nt (µ
A)
Drain Voltage (V)
Vg-Vth=1.0 V
Vg-Vth= -1.0 V
0.8 V
0.6 V
0.4 V
0.2 V
(a)
10-12
Gate Voltage (V)
pFET nFET
(b)
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
Dra
in C
urre
nt (A
)
Vd=-50mV
Vd=-1V
Vd=50mV
Vd=1V
On/Off>106、60uA/wire
Recent results to be presented by ESSDERC 2010 next week in Sevile
Wire cross-section: 20 nm X 10 nm
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
(5)
(5)
(10)
(10)(12)
(12x19)
(12)
(12x19)
(13x20)
(9x14)(10)
(10)
(10)
(8)
(8)
(16)
(13)
(34)
(3)(3)
(30)
(19)
VDD: 1.0~1.5 V
括弧内は寸法を示す
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
(5)
(5)
(10)
(10)(12)
(12x19)
(12)
(12x19)
(13x20)
(9x14)(10)
(10)
(10)
(8)
(8)
(16)
(13)
(34)
(3)(3)
(30)
(19)
VDD: 1.0~1.5 V
括弧内は寸法を示す
(12)
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
(5)
(5)
(10)
(10)(12)
(12x19)
(12)
(12x19)
(13x20)
(9x14)(10)
(10)
(10)
(8)
(8)
(16)
(13)
(34)
(3)(3)
(30)
(19)
VDD: 1.0~1.5 V
括弧内は寸法を示す
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
(5)
(5)
(10)
(10)(12)
(12x19)
(12)
(12x19)
(13x20)
(9x14)(10)
(10)
(10)
(8)
(8)
(16)
(13)
(34)
(3)(3)
(30)
(19)
VDD: 1.0~1.5 V
括弧内は寸法を示す
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
(5)
(5)
(10)
(10)(12)
(12x19)
(12)
(12x19)
(13x20)
(9x14)(10)
(10)
(10)
(8)
(8)
(16)
(13)
(34)
(3)(3)
(30)
(19)
VDD: 1.0~1.5 V
括弧内は寸法を示す
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
010203040506070
1 10 100 1000Gate Length (nm)
I ON
(µA
/ w
ire)
nMOSpMOS
(5)
(5)
(10)
(10)(12)
(12x19)
(12)
(12x19)
(13x20)
(9x14)(10)
(10)
(10)
(8)
(8)
(16)
(13)
(34)
(3)(3)
(30)
(19)
VDD: 1.0~1.5 V
括弧内は寸法を示す
(12)
本研究で得られたオン電流
(10x20)102µA
Our Work
Bench Mark
Bench MarkBench MarkThis work Ref[11] Ref[12] Ref[13] Ref[14] Ref[15] Ref[4]
NW Cross-section (nm) Rect. Rect. Rect. Cir. Cir. Elliptical Elliptical NW Size (nm) 10x20 10x20 14 10 10 12 13x20
Lg (nm) 65 25 100 30 8 65 35EOT or Tox (nm) 3 1.8 1.8 2 4 3 1.5
Vdd (V) 1.0 1.1 1.2 1.0 1.2 1.2 1.0Ion(uA) per wire 60.1 102 30.3 26.4 37.4 48.4 43.8
Ion(uA/um) by dia. 3117 5010 2170 2640 3740 4030 2592Ion(uA/um) by cir. 1609 2054 430 841 1191 1283 825
SS (mV/dec.) 70 79 68 71 75 ~75 85DIBL (mV/V) 62 56 15 13 22 40-82 65
Ion/Ioff ~1E6 >1E6 >1E5 ~1E6 >1E7 >1E7 ~2E5
Ref[11] by Stmicro Lg=25nm,Tox=1.8nmThis work Lg=65nm,Tox=3nm
Y. Jiang, VLSI 2008, p.34H.-S. Wong, VLSI 2009, p.92
S. Bangsaruntip, IEDM 2009, p.297C. Dupre, IEDM 2008, p. 749S.D.Suk, IEDM 2005, p.735G.Bidel, VLSI 2009, p.240
SiナノワイヤFET
Planer FETS. Kamiyama, IEDM 2009, p. 431
P. Packan, IEDM 2009, p.659
1.2~1.3V
1.0~1.1V
Lg=500~65nm
IIONON/I/IOFF OFF Bench markBench mark
This work
116
H2 annealingChapter 4
10 nm10 nm
H2 annealing750oC, 2min
1012 1013100El
ectr
on m
obili
ty µ
elec
[cm
2 /Vs]
400
300
Ninv [cm-2]
200
1012 1013100El
ectr
on m
obili
ty µ
elec
[cm
2 /Vs]
400
300
Ninv [cm-2]
200
1012 1013
Hol
e m
obili
ty µ
hole
[cm
2 /Vs]
Ninv [cm-2]
1009080706050
1012 1013
Hol
e m
obili
ty µ
hole
[cm
2 /Vs]
Ninv [cm-2]
1009080706050
w/o H2 anneal
w H2 anneal
w/o H2 anneal
w H2 anneal
Change the cross sectionA little improvement of surface roughness
Increase of coulomb scattering
µsrµsr
µcbµcb
117
Frequency, f [MHz]
I cp[x
10-
2A/
cm2 ]
4
2
0
10
12
20.50 1 1.5
6
8
Interface trap density (Dit)Chapter 4
The p+ region actsas a ‘substrate’ contact.
Gated diode
10 nm
Dit [eV-1cm-2]6.39 x 1011
w H2annealBOX
N+ P+
VR
Trapezoidal pulse+Vbase
ICP
ICP=q2fWLDit∆ψs
Gate
NWsBOX
N+ P+
VR
Trapezoidal pulse+Vbase
ICP
ICP=q2fWLDit∆ψs
Gate
NWs
10 nm
w/o H2anneal
Dit [eV-1cm-2]2.24 x 1011
Increase of interface trap density
3. Problems
118
We have to decrease Si layer thickness to better control of channel potential by gate bias.
Significant decrease in conduction or Ion.
ShortShort--channel effectchannel effectT. Skotnicki, IEDM 2009 Short Course (STMicroelectronics)
119
DrainDrain--induced barrier loweringinduced barrier loweringT. Skotnicki, IEDM 2010 Short Course (STMicroelectronics)
120
SubSub--threshold Slopethreshold SlopeT. Skotnicki, IEDM 2010 Short Course (STMicroelectronics)
110 mV/dec
85 mV/dec
75 mV/dec
65 mV/dec
95 mV/dec
121
3. Problems
122
Mobility degradation.
S. Bangsaruntip et al., pp.297, IEDM2009 (IBM), K. Tachi et al., pp.313, IEDM2009 (CEA-LETI)
Decreasing the diameter of NW
Problems in MultiProblems in Multi--gategate
Improvedshort-channel control
Severe mobility degradation
Significant µ degradationat diameter < 10 nm
Need to decrease diameter for SCH
123
K. Uchida et al., pp.47, IEDM2002 (Toshiba)
Problems in SOIProblems in SOI
Mobility is also decreased with decreasing the Si thickness of SOI transistor similar to the NW transistor. 124
When wire diameter becomes less than 10 nm, sudden drop of IdProblem for nanowire
IdDiameter
10 nm
2. Electron density decrease
If diameter cannot be scaled, SCE cannot be suppressed.
Then, again aggressive EOT scaling of high-k is necessary. 125
< 10 nm1. Mobility degradation
Extremely small distance between the electron and all around Si surface.
Strong scattering of electrons by interaction with all around Si surface.
Decrease of DOS in extremely narrow wire.
3. Problems
126
Carrier density degradation.
Number of quantum channels
Energy band of Bulk Si
Eg
By Prof. Shiraishi of Tsukuba univ.
Energy band of 3 x 3 Si wire
4 channels can be used
Eg
127
128By Profs. Oshiyama and Iwata, U. of Tokyo
Diameter dependence1 nm 2 nm 3 nm 4 nm 6 nm
By Profs. Oshiyama and Iwata, U. of Tokyo
Wire cross section dependence.
What cross section gives best solution forSCE suppression and drive current?.
129
J. B. Chang et al., pp.12, VLSI2012 (IBM)
VVthth variabilityvariability
nFETs pFETs
Significant increase in Vth variability with decreasing Fin width
130
K. Kim, pp.1, IEDM2010 (Samsung)1.21.1
1
0.9
0.8
0.7
0.6
0.5
EO
T [n
m]
202020152010Year
12
10
8
6
4
2
0
Body Thickness [nm
]
Multi-Gate
Planar
ITRS2011
Fin width
Trend 1
Trend 2
Trend 3 ?
EOT Scaling TrendsEOT Scaling Trends
Smaller wire/fin width is necessary for SCE suppression
But mobility and ION severely degrade with wire/fin width reduction
Therefore even in multi-gate structures, EOT scaling should be accelerated to provide SCE immunity 131
High-k beyond 0.5 nm
132
Limit in tLimit in toxox thinningthinning
R.Chau, et al., (Intel) IWGI 2003
133
Gate oxide should be thicker than mono atomic layer
0.8 nm gate oxide thickness MOSFETs operate0.8 nm Distance of 3 Si atoms 2 mono layers
Limit in tLimit in toxox thinningthinningR.Chau, et al., (Intel) IWGI 2003
1 0.010.1
1
10
100
1000
0.1
0.01
0.001
Pow
er D
ensi
ty [W
/cm
2 ]
Gate Length [µm]
Active Power
Passive PowerGate
Leakage
Gate Leakage Power Density becomes significantly large with Lg reduction, and thus, with tox thinning!!
W.F.Clark, (IBM) VLSI 2007 Short Course
134
To use high-k dielectrics
Thin SiO2
Thick high-k dielectrics
Almost the same electric characteristics
However, very difficult and big challenge!
K: Dielectric Constant
5 times thicker
Small leakageCurrent
K=4K=20
SolutionSolution
SiO2 High-k
135
Equivalent Oxide Thickness (EOT)Equivalent Oxide Thickness (EOT)
Silicon Substrate
S D
Silicon Substrate
S D
SiO2
Poly-Si
C Poly
COX
CSi
High-kCOX
CSi
Equivalent Oxide Thickness (EOT): gate dielectrics itself, Cox
Capacitance Equivalent Thickness (CET): entire gate stack,
Metal gate can eliminate the poly-Si depletion.
Inversion CET = Tinv ≈ EOT + 0.4nm with metal gate electrode
Metal
Cmetal
Poly-Si(1020cm-3)
K. Natori, et al., (Tsukuba Univ) SSDM 2005, p.286
CMetal(EOT: 0.1 nm)
Depletion
Cmetal is finite because of quantum effect. In other words electron is not a point charge
located at the interface but distributed charge.
(EOT: 0.3 nm)
Combination of high-k and metal gate is important
136
R. Hauser, IEDM Short Course, 1999Hubbard and Schlom, J Mater Res 11 2757 (1996)
Gas or liquidat 1000 K
H
Radio activeHe
Li BeB C N O F Ne
① Na Mg Al Si P S Cl Ar
② ① ① ① ① ① ① ① ① ① ① K Ca Sc Ti V Cr Mn Fc Co Ni Cu Zn Ga Ge As Se Br Kr ① ① ① ① ① ① ① ① ① ① Rh Sr Y Zr Nb Mo Tc Ru Rb Pd Ag Cd In Sn Sb Te I Xe ③ ① ① ① ① ① ① ① Cs Ba
HfTa W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Rf Ha Sg Ns Hs Mt
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er TmYb Lu Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
Candidates
Na Al Si P S Cl Ar
② ① ① ① ① ① ① ① ① ① K Sc Ti V Cr Mn Fc Co Ni Cu Zn Ga Ge As Se Br Kr ① ① ① ① ① ① ①
Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
②
③
Unstable at Si interfaceSi + MOX M + SiO2①
Si + MOX MSiX + SiO2
Si + MOX M + MSiXOY
Choice of High-k elements for oxide
HfO2 based dielectrics are selected as the
first generation materials, because of
their merit in1) band-offset,
2) dielectric constant3) thermal stability
La2O3 based dielectrics are
thought to be the next generation materials, which may not need a
thicker interfacial layer
137
0 10 20 30 40 50Dielectric Constant
4
2
0
-2
-4
-6
SiO2
Ban
d D
isco
ntin
uity
[eV]
Si
XPS measurement by Prof. T. Hattori, INFOS 2003
Conduction band offset vs. Dielectric Constant
Band offset
Oxide
Leakage Current by Tunneling
138
SiO2-ILHfSix (k~4)
VO
IO
IOVO
VO
IOIO
VOHfO2
Si substrate SiO2-IL(k~4)
LaSix
VO
IOVO
IO
VO
IOLa2O3silicate
La-rich Si-rich
Si substrate
High PO2Low PO2 High PO2Low PO2
HfO2 case La2O3 case
Direct contact can be achieved with La2O3 by forming silicate at interfaceControl of oxygen partial pressure is the key for processing.
Our approach
K. Kakushima, et al., VLSI2010, p.69
Direct high-k/Si by silicate reaction
SiO2-ILHfSix (k~4)
VO
IO
IOVO
VO
IOIO
VOHfO2
Si substrate SiO2-IL(k~4)
LaSix
VO
IOVO
IO
VO
IOLa2O3silicate
La-rich Si-rich
Si substrate
High PO2Low PO2 High PO2Low PO2
SiO2 IL formation
Si substrate
silicate formation
Si substrate
HfO2 case La2O3 case
Direct contact can be achieved with La2O3 by forming silicate at interfaceControl of oxygen partial pressusre is the key for processing.
Our approach
K. Kakushima, et al., VLSI2010, p.69
Direct high-k/Si by silicate reaction
1837184018431846Binding energy (eV)
Inte
nsity
(a.u
)
Si sub.
Hf SilicateSiO2
500 oC
1837184018431846Binding energy (eV)
Inte
nsity
(a.u
)
Si sub.
Hf SilicateSiO2
500 oC
SiOx-IL
HfO2
W
1 nm
k=4
k=16
SiOx-IL growth at HfO2/Si Interface
HfO2 + Si + O2→ HfO2 + Si + 2O*→HfO2+SiO2
Phase separator
SiOx-IL is formed after annealingOxygen control is required for optimizing the reaction
Oxygen supplied from W gate electrode
XPS Si1s spectrum
D.J.Lichtenwalner, Tans. ECS 11, 319
TEM image500 oC 30min
H. Shimizu, JJAP, 44, pp. 6131
La-Silicate Reaction at La2O3/Si
La2O3
La-silicate
W
500 oC, 30 min
1 nm
k=8~14
k=23
1837184018431846Binding energy (eV)
Inte
nsity
(a.u
)
as depo.
300 oC
La-silicate
Si sub.
500 oC
1837184018431846Binding energy (eV)
Inte
nsity
(a.u
)
as depo.
300 oC
La-silicate
Si sub.
500 oC
La2O3 + Si + nO2→ La2SiO5, La2Si2O7,
La9.33Si6O26, La10(SiO4)6O3, etc.La2O3 can achieve direct contact of high-k/Si
XPS Si1s spectra TEM image
Direct contact high-k/Si is possible
5m
Robot
Flash Lamp
ALDRTAEntrance
Sputterfor MG
EB Deposition for HK5m
Cluster tool for HKMG Stack
143
Cluster Chambers for HKMG Gate Stack
Flash Lamp Anneal
EB Deposition: HK Sputter: MG
ALD: HK
Robot
RTA
Entrance
144
145
Shutter movement
Chip
Si Si SiSi
Metal Metal Metal Metal
Thin Thick
high-k
15cm
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
3.5E-03
0 0.2 0.4 0.6 0.8 1
Vg=0VVg=0.2VVg=0.4VVg=0.6VVg=0.8VVg=1.0VVg=1.2V
0 0.2 0.4 0.6 0.8 1
Vg=0VVg=0.2VVg=0.4VVg=0.6VVg=0.8VVg=1.0VVg=1.2V
0 0.2 0.4 0.6 0.8 1
Vg=0VVg=0.2VVg=0.4VVg=0.6VVg=0.8VVg=1.0VVg=1.2VI d
(V)
Vth=-0.04VVth=-0.05VVth=-0.06V
Substrate
Moving Mask
SourceElectron Beam
Flux
Deposited thin film
146
147
148
L=0.5~100µm (8 kinds)W=10, 20, 50, 100µm(4 kinds)
30 different Trs
26 c
hips
1cm
1cm
1cm×1cm
p-Si
S Dn+ Sn+SiO2
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
0 0.5 1 1.5 2 2.5 3
EOT ( nm )
Cur
rent
den
sity
( A
/cm
2 )Al2O3HfAlO(N)HfO2HfSiO(N)HfTaOLa2O3Nd2O3Pr2O3PrSiOPrTiOSiON/SiNSm2O3SrTiO3Ta2O5TiO2ZrO2(N)ZrSiOZrAlO(N)
Gate Leakage vs EOT, (Vg=|1|V)
La2O3
HfO2
149
150
2
1.5
1
0.5
0
Cap
acita
nce
[µF/
cm2 ]
-1 -0.5 0 0.5 1Gate Voltage [V]
10kHz 100kHz 1MHz
20 x 20µm2 1.5
1
0.5
0
Cap
acita
nce
[µF/
cm2 ]
-1.5 -1 -0.5 0 0.5Gate Voltage [V]
20 x 20µm2
10kHz 100kHz 1MHz
2
1.5
1
0.5
0
Cap
acita
nce
[µF/
cm2 ]
-1.5 -1 -0.5 0 0.5Gate Voltage [V]
20 x 20µm2
10kHz 100kHz 1MHz
FGA500oC 30min FGA700oC 30min FGA800oC 30min
A fairly nice La-silicate/Si interface can be obtained with high temperature annealing. (800oC)
However, high-temperature anneal is necessary for the good interfacial property
substrate
①La gas feed
②Ar purge ③H2O feed
④Ar purge
Laligand H
O
substrate substrate substrate
1 cycle
La
C 3H7
3
L a
C 3H7
3
L a
C 3H7
3
CLaN
NH
C3H7
C3H7
La(iPrCp)3 La(FAMD)3
Precursor (ligand)
ALD is indispensable from the manufacturing viewpoint- precise control of film thickness and good uniformity
K. Ozawa, et al., (Tokyo Tech. and AIST) Ext. Abstr. the 16th Workshop on Gate Stack Technology and Physics., 2011, p.107.
151
ALD of La2O3
152
① silicate-reaction-formedfresh interface
metal
Si sub.
metal
Si sub.
La2O3 La-silicateSi Si
Fresh interface with silicate reaction
J. S. Jur, et al., Appl. Phys. Lett., Vol. 87, No. 10, (2007) p. 102908
② stress relaxation at interface by glass type structure of La
silicate.
La atomLa-O-Si bonding
Si sub.
SiO4tetrahedron network
FGA800oC is necessary to reduce the interfacial stress
S. D. Kosowsky, et al., Appl. Phys. Lett., Vol. 70, No. 23, (1997) pp. 3119
Physical mechanisms for small DitPhysical mechanisms for small Dit
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
600 700 800 900 1000As depo
~ ~
Annealing temperature (oC)
EOT
(nm
)
Annealed for 2 sLa2O3(3.5 nm)
W(60 nm)
TiN/W(12 nm)
TiN/W(6 nm)
TiN(45nm)/W(6nm)
00.5
11.5
22.5
33.5
44.5
-1 -0.5 0 0.5
Vg (V)
Cg
(uF/
cm2 )
Experiment
Cvc fittingTheory
EOT=0.55nm
TaN/(45nm)/W(3nm)900oC, 30min
EOT=0.55nm
153
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.5 0.55 0.6 0.65 0.7
Flat
-ban
d vo
ltage
(V)
EOT(nm)
TaN(45nm)/W(3nm)
900oC, 30min
Qfix=1×1011 cm-2
Fixed Charge density: 1×1011 cm-2
154
0 0.2 0.4 0.6 0.8 1.0
Drain Voltage (V)
0.2
0.4
0.6
0.8
1.0
Dra
in C
urre
nt (m
A)
Vg= 0.4V
Vg= 0.6V
Vg= 0.8V
Vg= 1.0V
Vg= 0.2V
Vg= 0 V
L/W = 5/20µm
T = 300K
Nsub = 3×1016cm-3
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5
EOT = 0.40nm
L/W = 5/20µm
T = 300K
Nsub = 3×1016cm-3
Eeff [MV/cm]
Elec
tron
Mob
ility
[cm
2 /Vse
c]
EOT=0.40nm
Our Work at TIT: HighOur Work at TIT: High--k k
155
Our result at TIT
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0.3 0.4 0.5 0.6 0.7 0.8
ITRS requirement
J gat
1 V
(A/c
m2 )
EOT (nm)
Benchmark of LaBenchmark of La--silicate dielectricssilicate dielectrics
T. Ando, et al., (IBM) IEDM 2009, p.423
0
50
100
150
200
250
300
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1EOT (nm)
Mob
ility
(cm
2 /Vse
c)
at 1 MV/cm
Open square : Hf-based oxides
Solid circle: Our data
Our data: La-silicate gate oxide
La-silicate gate oxide
L.-Å. Ragnarsson, et al., (IMEC) Microelectron. Eng, vol. 88, no. 7, pp. 1317–1322, 2011.
156
Gate Leakage current Effective Mobility
Si-sub.
Metal
SiO2-IL
High-kSmall interfacial state
density at high-k/Si
Oxygen diffusion control for prevention of EOT increase
and oxygen vacancy formation in high-k
Thinning or removal of SiO2-IL for small EOT
Flat metal/high-k interface for better
mobility
O
Workfunction engineering for Vth control
Interface dipole control for Vth tuning
Suppression of oxygen vacancy
formation
Control of interface reaction and Si diffusion to high-k
Oxygen concentration control for prevention of EOT
increase and oxygen vacancy formation in high-k
Suppression of metal diffusion
Endurance for high temperature process
Remove contaminationintroduced by CVD
Reliability: PBTI, NBTI, TDDB
Suppression of gate leakage current
Suppression of FLP
157
Issues in high-k/metal gate stack
Si benchmark (nMOSFET)Si benchmark (nMOSFET)
158
EOT Mobility Vth SS DIBLGate stack Ref.
0.45nmTiN/Cap/HfO2 115cm2/Vs
(at 1x1013cm-2)IMEC
MEE20110.3V
(Lg=10um)
0.52nmTiN/Cap/HfO2 110cm2/Vs
(at 1x1013cm-2)IBM
VLSI2011~0.4V
(Lg=24nm) 90mV/dec 147mV/V
0.59nmMetal/HfO2 130cm2/Vs
(at 1MV/cm)0.45V
(Lg=1um) 75mV/decSematechVLSI2009
0.65nmMetal/Hf-basedSamsungVLSI2011
0.3~0.4V(Lg=~30nm) 90mV/dec 100mV/V
0.95nmMetal/Hf-basedIntel
IEDM2009~0.3V
(Lg=30nm) 100mV/dec ~200mV/V
0.62nmW/La-silicateTokyo Tech.T-ED2012
-0.08V(Lg=10um) ~70mV/dec
155cm2/Vs (at 1MV/cm)
0.55nmTiN/Cap/HfO2 140cm2/Vs
(at 1MV/cm)IBM
VLSI2009
159
Conclusions 1
Downsizing of MOSFETs is still important for high-speed low-power operation of logic LSIs.
Ioff will limit the downsizing.
Punchthrough component of Ioff will be suppressed by thinning tox and adopting new configuration such as FinFET or nanowire FET.
Direct tunneling will limit the downsizing @Lg = 3 nm.
Even before that, subthreshould leakage would limit the downsizing @ Lg > 3nm, depending on the application.
160
Conclusions 2
In the application, Ion/Ioff ratio is important.
The ratio is typically 106 for the present devices, however, it degrades significantly with decreasing the supply voltage.
Si nanowire FET has advantage not only on Ioff over planer FET, but also on Ion, because of better mobility and higher channel carrier density.
In order to suppress Ioff with decrease in Lg, the diameter of nanowire, width of fin, or thickness of Si film of SOI need to be shirked.
.However, with decreasing the above diameter, width or thickness less than several nano-meter, very significant decrease in Ion occurs, because of the degradation on mobility and carrier concentration.
161
Conclusions 3
If the diameter, width or thickness cannot be decreased, we need to decrease the EOT of high-k aggressively in order to suppress Ioff.
High-k EOT reduction trend is very slow – 0.05 nm for each generation --, for the moment.
The limit of EOT scaling is expected to be around 0.4 nm or so, considering the additional capacitances of channel and metal gate.
By changing the high-k material from HfO2 to La-silicate, we can obtain the good operation of MOSFET with EOT = 0.4 nm,
.Metal silicide Shottoky S/D will become important in order to suppress the S/D encroachment to the channel by dopant diffusion.
162
Conclusions 3
.
Downsizing of MOFET is becoming more and more important for low power high performance application in the future smart society, and will be accomplished in another 10 to 15 years, although the rate of the downsizing will become slow.
Thus, many challenging technology development will be necessary for another 10 to 15 years.
Thank you very much for your attention.