special topics in nanodevices
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2007. 1. Special Issues on Nanodevices 1
Special Topics in Nanodevices
3rd Lecture: Nanowire MOSFETs
Byung-Gook Park
2007. 1. Special Issues on Nanodevices 2
Nanowire MOSFETs
MOSFET Scaling and Issues
Evolution of MOSFET Device Structure
Double Gate Structures
Multiple Gate Structures
Ballistic Electron Transport in Nanowires
Effect of Scattering – Landauer’s Formula
Ref : H.S. Min, Y.J. Park, B.G. Park, H.C. Shin, Semiconductor Devices with NANOCAD, Ch. 8
S. Datta, Electronic Transport in Mesoscopic Systems, Ch. 2
2007. 1. Special Issues on Nanodevices 3
MOSFET Scaling - The Grand View
1
10
100
1960 1980 2000 2020
Year
0.1
0.01
Ave
rage
Des
ign
Ru
le ( m
)
SIA Roadmap ’94
SIA Roadmap ’97
ITRS (DRAM) ’05
ITRS (MPU) ’05
D.R. = 20e - 0.116(Y-1960)
~ 3 yrs : 2-1/2 reduction ~ 20 yrs : 10-1 reduction
ITRS Roadmap (’05)
2016 : 9 nm (MPU Lphy)
2019 : 6 nm (MPU Lphy)
2007. 1. Special Issues on Nanodevices 4
Short Channel Effects (1)
Phenomenon : roll-off of VT as a function of gate length L
VT
L
Cause : charge sharing
2007. 1. Special Issues on Nanodevices 5
Short Channel Effects (2)
L'
S D
L
B
G L'
w s
w p
x j
w c
x D
)]1/21)(/(1[2 jDjox
dFFBT xxLx
C
QVV
V VQ
CT FB Fd
ox
2
Q L QL L
d d 2 w c = x D 로 두 고 공 핍 층
모 양 을 S / 과 동 심 원 으 로 가 정 하 면
( ) ( )x x x w xj D j s D 2 2 2 w x x x x
x x x
s j D D j
j D j
( )
/( )
2 2
1 2 1
Q Q w L
Q x L x x
d d s
d j D j
( / )
[ ( / )( / )]
1
1 1 2 1
2007. 1. Special Issues on Nanodevices 6
Number of dopants in the depletion region :- The number of dopant atoms in the depletion region decreases as the device dimension decreases.- As the number of dopants decreases, the statistical fluctuation of the number of dopants becomes more important.
Example : L = W = 50 nm, Na = 1018 cm-3
Wdm = 35 nm N = Na LWWdm = 87.5
sN = N1/2 = 9.35 (~ 10.7%)
Threshold voltage variation due to dopant number fluctuation :
NN
N
NN 1
LW
WN
C
q dma
oxVT 3
Dopant Number Fluctuation and VT
2007. 1. Special Issues on Nanodevices 7
Evolution of Device Structure (1)
Tightness of gate control over the channel
SiO2
Double gateSOIBulk
2007. 1. Special Issues on Nanodevices 8
Evolution of Device Structure (2)
Tightness of gate control over the channel
2007. 1. Special Issues on Nanodevices 9
Short Channel Effects
<Single gate> <Double gate>
Design guideline
SG: tsi Lchannel/3
DG: tsi 2Lchannel/3
NW: tsi Lchannel
2007. 1. Special Issues on Nanodevices 10
Various Double Gate Structures
S D
S
D
S
D
L: horizontalW: horizontal
L: verticalW: horizontal
L: horizontalW: vertical
Type I Type II Type III
2007. 1. Special Issues on Nanodevices 11
FinFETs
G
SD
LG
tSOI
Wfin
G
SD
LG
SOI
Wfin
S DG
G
G
G
S D
FinFET Schematic FinFET Issue
Hfin=tSOI
Wfin<LG
2007. 1. Special Issues on Nanodevices 12
Electric Field and Charge Distribution
Electric Field
Charge
Eof
Eob
qNA Qnf Qnb
Eof
Eob
VG>VTVG<VT
2007. 1. Special Issues on Nanodevices 13
Basic Equations for DGMOSFETs
oobof ttt
Due to symmetry
oobof CCC
obobobofofof VtEtEV
Voltage, electric field, and channel charge
so
sobof QEE
2
1
bcfs QQQ 2
2007. 1. Special Issues on Nanodevices 14
Threshold Voltage and Drain Current
Threshold voltage
o
bFFBT C
QVV
2
12
Drain current
2
2
12DDTGonD VVVVC
L
WI
* Usually, Qb 0 to suppress the dopant # fluctuation effect
negative threshold voltage for n-channel
work function engineering required
* Two devices in one!
2007. 1. Special Issues on Nanodevices 15
Inversion Charge in the Channel
Charge distribution :
- assumption: Charge distribution is dominated by the ground state.
Surface inversion – two channels are separated
<Thick channel>
<Thin channel>
Bulk inversion – two channels are merged
2007. 1. Special Issues on Nanodevices 16
VT vs. Channel Thickness
VT
Tch
Threshold voltage for
thicker channel :
o
bFFBT C
QVV
2
12
Threshold voltage for
thin channel :
- dominated by the energy
level quantization
- higher for thinner body
2007. 1. Special Issues on Nanodevices 17
MG MOSFETs and Corner Effects
Gate
Oxide
Channel
Gate
Oxide
Channel
Quadruple gate MOSFET
- The gate surrounds the
channel.
Corner effect :
- Field concentration at
corners.
2007. 1. Special Issues on Nanodevices 18
Coaxial Gate MOSFETs
Gate
Oxide
Channel
Ideal shape for NW MOSFET
- No corner effect
- 2D analysis with cylindrical coordinates
2007. 1. Special Issues on Nanodevices 19
Carbon Nanotube FETs
CNT FETs
- Schottky contact at S/D junction- High dielectric for gate
insulator
2007. 1. Special Issues on Nanodevices 20
Ballistic Transport in Nanowire (1)
Contact 1 Contact 2
W
LBallistic Conductor
x
y
Large conductor (L >> mean free path): G = W/L (Ohmic scaling)
G for L 0?
Ballistic conductor (L << mean free path): G Gc for L 0 Gc
“contact” resistance
2007. 1. Special Issues on Nanodevices 21
Assumption : ‘reflectionless contacts’Electrons can enter a wide contact from a narrow conductor without suffering reflections.=> +k states : occupied by electrons originating in the left contact k states : occupied by electrons originating in the right contact
Quasi-Fermi levels :
Dispersion relation :
N : transverse mode number N : cut-off energy for mode N
2, eVEeVE ff 1
Nmk
kNE *
22
2),(
k
E N = 3 2 1
1
2
3
eV1eV2
Ballistic Transport in Nanowire (2)
2007. 1. Special Issues on Nanodevices 22
Number of transverse modes :
Current by a single transverse mode : +k states are occupied according to the function f(EEf
+)
N
NEEM )()(
kf
kf
EEfkE
Le
EEvfLe
envI
)(1
)(
k
dkL2
spin)2(for
dEEEfhe
I f )(2
Ballistic Transport in Nanowire (3)
2007. 1. Special Issues on Nanodevices 23
Current by multiple transverse modes :
dEEMEEfhe
I f )()(2
Total current :
dEEMEEfEEfhe
III
ff )()]()([2
At low temperature : )()( EEEEf ff
MVVhe
MEEhe
I ff )(2
)(2
12
2
Mhe
Gc
22
MMe
hGc
k9.12
2 21
Ballistic Transport in Nanowire (4)
2007. 1. Special Issues on Nanodevices 24
Landauer’s Formula (1)
Contact 1 Contact 2Conductor
x
yTLead 1 Lead 2
)1( TMVVhe
I
MTVVhe
I
MVVhe
I
)(2
)(2
)(2
12
2
1
12
2
2
12
2
1
2007. 1. Special Issues on Nanodevices 25
Landauer’s Formula (2)
MTVVhe
IIII )(2
12
2
211
MThe
G22
Contact 1 Contact 2Conductor
x
yTLead 1 Lead 2
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