Low-Frequency Noise in Nanoscale Ballistic Transistors · Nanotube FET – a single charge in gate...
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Low-Frequency Noise in Nanoscale Ballistic Transistors Jerry Tersoff IBM T. J. Watson Research Center Stefan Heinze (Univ. Hamburg) Vasili Perebeinos, Phaedon Avouris
Transcript of Low-Frequency Noise in Nanoscale Ballistic Transistors · Nanotube FET – a single charge in gate...
Low-Frequency Noise in
Nanoscale Ballistic Transistors
Jerry TersoffIBM T. J. Watson Research Center
Stefan Heinze (Univ. Hamburg)Vasili Perebeinos, Phaedon Avouris
Nanoscale electronic devicesmolecular electronics; quantum dots & wireshigh density & performanceballistic, quantum coherent devices
Carbon nanotubesFETs – high performance by some measuresballistic transistors
Coherence length – inelastic scattering by phonons
Low frequency noise (RTS, 1/f ) – elastic scatteringby charge traps, even in ballistic transistors
Low-field – high mobility (Fuhrer 2004)
acoustic phonon coupling is small in 1D
High-field – current saturation (Dekker, Dai, McEuen 2004)
Transport modeling including interband scattering.Tight binding for electrons; improved phonon model;
Su-Schrieffer-Heeger model for e-ph coupling.
Coherence length Lk=vkτk
Up to 3 μm even at room temperature
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0
L
k (μ
m)
0.200.150.100.050.00
εk – εc (eV)
T = 10 K
T = 300 Kd = 2 nm
RBM
KLA
KLO
T = 10 KT = 300 K
d = 2 nm
Perebeinos, Tersoff, and Avouris, PRL 94, 086802 (2005).
Nanotube FET – a single charge in gate oxide gives large effects
Wrap gate, oxide 15nm thick.Ballistic FET, NEGF calculation
Black line: no charge.Red: charge next to nanotube)
Wang, Heinze, and Tersoff, Nano Lett. 7, 910 (2007).
Nanotube FET – a single charge in gate oxide gives large effects
Wrap gate, oxide 15nm thick.Ballistic FET, NEGF calculation
Charges can trap/detrap, thermally activated
Static charge t shift in voltage threshold (large shifts are common in CNTs)Charge switching t random telegraph noise (can be over 50% in CNTs)Many switching t 1/f noise (unusually large for CNTs)
Black line: no charge.Red: charge next to nanotube)
Wang, Heinze, and Tersoff, Nano Lett. 7, 910 (2007).
Nanotube FET – a single charge in gate oxide gives large effects
Wrap gate, oxide 15nm thick.Ballistic FET, NEGF calculation
Black line: no charge.Red: charge next to nanotube)Black line: no charge.Red: charge next to nanotube)
fractional currentchange
Wang, Heinze, and Tersoff, Nano Lett. 7, 910 (2007).
“An astonishing variety of systems” show 1/f noise – Dutta & Horn
Noise spectrum
Arises from thermally activatedprocesses having a range ofactivation energies.
E.g. charge trapping in MOS-FETs(and presumably in CNT-FETs)
f~If
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Smaller system t larger noise, problem for nanoscale.
F. N. Hooge (1969) — Empirical rule for noise:A = αH / N, N is the number of carriers in the system
Correct scaling to characterize a homogeneous material.Plausible for FET as vary Vg, for diffusive transport.
As devices shrink, eventually t ballistic. Different scaling?
Here, consider noise in nanoscale ballistic FETsSuggests ballistic is different than diffusiveExplicit model for how noise varies with Vg
Compare with recent “quasi-ballistic” results of Lin et al.
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Top Gate @ +2V
Ground Plane
Nanotube
Nanotube Schottky-barrier FET (Heinze et al., PRL 2002)
10-9
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10-7
10-6
10-5
10-4
Con
duct
ance
(S)
151050Top Gate Voltage (V)
Contact 5nmOxide 60nm
Oxide 120nmContact 50nm
Current is controlled by Schottky barrier at contactFocus on subthreshold regime :
most important; largest noise; simplest.
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( )gEII =0 ( ))t(EEII g δ+=
( ))t(EEII g δ+=
Looks like noise in Vg
S/VE gg =
( )( ) )t(E
dVdISS/VI
)t(ES/VII
gg
g
δ
δ
+≈
+=
I0 amplification intrinsicfactor noise
( ))t(ESVII g δ+=
)t(EdVdISII
g
δ+≈ 0
( )fA
III
=−
20
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( )f
E2
2 γδ =
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
gdVIlndSA γ
[ redefine γS t γ ]
Assumed Id limited by tunneling at contact
Don’t need to assume ballistic channel,only that channel resistance negligible[e.g. subthreshold Vg & large barrier]
Neglects lots of real effects, e.g. γ may depend on Vg
Just take known device physics & work forward
Strong prediction – only unknown is overall coefficient
2
2
⎟⎟⎠
⎞⎜⎜⎝
⎛=
gdVIlndA γ
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-10
1E-9
1E-8
1E-7
Vg (V)
Lin et al. CNT SB-FET
I d (A
)
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-4
1E-3
0.01
0.1
nois
e A
Vg (V)
Yu-Ming Lin et al. NanoLett. 2006
“quasi-ballistic” CNT SB-FET
Fit Id vs Vg to smooth function,to allow taking derivative.
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-10
1E-9
1E-8
1E-7
Vg (V)
Lin et al. CNT SB-FET
I d (A
)
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-4
1E-3
0.01
0.1
nois
e A
Vg (V)
2
2
dId⎟⎟⎠
⎞⎜⎜⎝
⎛=
gVlnA γ
One unknown parameter, γ
Fits data well over 2 orders of magnitude
What about “on” regime?
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-10
1E-9
1E-8
1E-7
Vg (V)
Lin et al. CNT SB-FET
I d (A
)
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-4
1E-3
0.01
0.1
nois
e A
Vg (V)
2
2
dId⎟⎟⎠
⎞⎜⎜⎝
⎛=
gVlnA γ
Assumed Id controlled by contact.
Channel t noisy resistor in series,or transmission T<1.
2
2
2
dId
dcg
IVlnA αγ +⎟
⎟⎠
⎞⎜⎜⎝
⎛=
( )2dccc V/RA=α
Measured Id reflects total resistance of contact and channel in series.
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-10
1E-9
1E-8
1E-7
Vg (V)
Lin et al. CNT SB-FET
I d (A
)
-1.5 -1.0 -0.5 0.0 0.5 1.0
1E-4
1E-3
0.01
0.1
nois
e A
Vg (V)
Prediction:
Crude, but physics-based, surprisingly successfulDescribes subthreshold noise of 2 quite different devicesShould apply to any ballistic, single-channel device.I.e. any sufficiently small device?Results for CNTs may have broader implications for
understanding any future nano/ballistic technology.
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2
dId⎟⎟⎠
⎞⎜⎜⎝
⎛=
gVlnA γ
Why are carbon nanotubes so noisy?Single channel (noise scales like 1/ Nchannel )A single charge can drastically affect I dPoor oxide quality – bare oxide surface
(cf Si MOS-FET – Si-SiO2 is special)
Any sufficiently small device…
What is to be done?
Gate Dielectric
Dielectric ε unimportant for CNT SB-FET.Choose dielectric to minimize noise.Vacuum ideal (but want large field at contact).Quasi-2D layered materials with passive surface.
Number of channels: fewer isn’t necessarily better
Capacitance is dominated byparasitic C of metal leads.
Number of channels: fewer isn’t necessarily better
Capacitance is dominated byparasitic C of metal leads.
N in parallel reduces noise by 1/N.Increases current by N.Same C, so increases device speed.
1/ f noise in nanoscale ballistic transistors
Generic model for oxide traps:act like 1/ f noise in Vg
Simple prediction; consistent with data for CNT-FETs
1/N never appears in analysis
Ballistic is simpler than diffusive, major opportunity for CNTs
Relevant for other future nano/ballistic technologies
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2
dId⎟⎟⎠
⎞⎜⎜⎝
⎛=
gVlnA γ
