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

15

10

5

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

12

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.

200

150

100

50

0

Hei

ght (

nm)

200150100500Length (nm)

Source

Top Gate @ +2V

Ground Plane

Nanotube

Nanotube Schottky-barrier FET (Heinze et al., PRL 2002)

10-9

10-8

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.

200

150

100

50

0

200150100500Length (nm)

Source

Top Gate @ +2V

Ground Plane

Nanotube

200

150

100

50

0

Hei

ght (

nm)

200150100500Length (nm)

Source

Top Gate @ +2V

Ground Plane

Nanotube

( )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

20

( )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.

2

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

2

2

dId⎟⎟⎠

⎞⎜⎜⎝

⎛=

gVlnA γ