Carbon nanotubes as ultrahigh-Q mechanical resonators at 300MHz - - PowerPoint PPT Presentation

Carbon nanotubes as ultrahigh-Q mechanical resonators at 300MHz

Andreas K. H¨ uttel∗, Gary A. Steele, Benoit Witkamp, Menno Poot Leo P . Kouwenhoven, Herre S. J. van der Zant

400 nm

I (pA)

~2cm

• 64.5 dBm

u(t)

A

Vsd Vg

E(t)

(MHz) VRF Q=140670 88 87 86 293.41 293.42 293.43

CNT

source drain 800 nm

gate ∗Present address: Institute for Experimental and Applied Physics,

University of Regensburg, Germany Solid State Based Quantum Information Processing — Herrsching, 2009

Nanotubes as beam resonators — up to now

complicated setup — even at 1K, maximally Q ≃ 2000

Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators Hsin-Ying Chiu, Peter Hung, Henk W. Ch. Postma and Marc Bockrath Nano Lett., 2008, 8 (12), pp 4342–434 Ultrasensitive Mass Sensing with a Nanotube Electromech. Resonator

• B. Lassagne, D. Garcia-Sanchez, A. Aguasca and A.

Bachtold Nano Lett., 2008, 8 (11), pp 3735–373

Why low Q?

Many possible reasons.

• HF cables directly to sample: heating, noise
• Contamination of the nanotubes during lithography
• Clamping points?

Chip fabrication and measurement setup

400 nm ~2cm

A

Vsd Vg

E(t)

VRF

CNT

source drain 800 nm

gate

• Basic chip geometry and fabrication as already shown by Georg G¨
• tz
• Additional wet-etch step to suspend the nanotube over full length
• All gate areas connected to a single gate voltage source Vg
• RF antenna suspended ∼ 2cm above chip
• Dilution refrigerator (T ≃ 20mK)
• Only dc measurement
• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

dc Coulomb blockade measurement — beautiful diamonds

0.5 1

• 4.4
• 4.2

I (nA)

• 4.0

Vg(V)

• 0.88
• 0.86
• 0.84
• 0.82
• 2

|I| (pA) 2 Vsd (mV)

1 10 100 1000 10000

Vg(V)

highly regular quantum dot within the nanotube

D Dot S D S

Vg

CB SET

D S

source dot gate

N el.

drain

Vg VSD I

• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

Fixed Vg and VSD, sweep of RF signal frequency

I (pA) I (nA) (MHz)

• 64.5 dBm

(MHz)

• 17.8 dBm

Q=140670

2 1 100 300 500 88 87 86 293.41 293.42 293.43 293.44

• Sharp resonant structure in Idc(ν)
• Very low driving power required
• From FWHM, Q ≃ 140000
• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

Vg dependence — this is really a mechanical resonance!

• 6
• 4
• 2

Vg (V) 150 200 250 300 (MHz)

10 100 1000

dI d

(pA/MHz)

(MHz) Vg (V)

150 200 250 300 350

• 6
• 5
• 4
• 3
• 2
• 1

red: continuum beam model

• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

Detection mechanism — mechanically induced averaging

1 2 1.5 285 305 (MHz) 0.6 285 305 (Mhz) I (nA) I (nA) Vg

ac,eff

I

• 5.22 -5.21
• 5.2
• 5.19

Vg (V)

Vg=−5.17V Vg=−5.16V

• at resonant driving the nanotube position oscillates
• oscillating Cg −

→ averaging over CB oscillations

• 5.22 -5.21
• 5.2
• 5.19

Vg (V) I (nA)

• 0.1

0.1

• 5.22 -5.21
• 5.2
• 5.19

Vg (V)

amplitude calculated from ( ) I V

DC g

Vg

ac,eff=1mV

measured resonance amplitude ( )

• Imax
• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

Some numbers

• Resonance frequency 120MHz ν 360MHz
• Zero-tension frequency consistent with CNT diameter from band gap
• Vg dependence of frequency consistent with bending vibration mode
• Quality factor up to Q ≃ 150000
• Estimated motion amplitude at resonant driving ∼ 250pm

compare thermal motion 6.5pm, zero-point motion 1.9pm

• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

Driving into nonlinear response...

I (pA) (MHz)

• 52.5 dBm

I (pA) I (pA)

80 mK, -70 dBm

• 62 dBm

I (pA)

• 56 dBm

I (pA)

• same temperature
• same working point Vg, VSD
• low driving power:

symmetric, “linear” response

• high driving power:

asymmetric response, hysteresis Duffing-like oscillator

• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

... and then increasing the temperature

• 53 dBm, 20mK

80mK 120mK 160mK

I (pA) I (pA) I (pA) I (pA) (MHz)

• same driving power
• same working point Vg, VSD
• low temperature:

asymmetric response, hysteresis Duffing-like oscillator

• high temperature:

symmetric, “linear” response peak broadening

• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

Temperature dependence of Q

• 66 dBm, 40mK

Q=123578 Q=23210

• 45 dBm, 1K

Q=59283

• 50.5 dBm, 320mK

(MHz) I (pA) I (pA) I (pA)

(a)

0.01

Q-factor Temperature (K)

0.1 1 10

4

10

5

(b) (c)

~T

• 0.36

Q(T) fits power law prediction for intrinsic dissipation in nanotube

− → H. Jiang et al., Phys. Rev. Lett. 93, 185501 (2004)

• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h

Summary & outlook, but no conclusion yet!

• Nanotube as light, extremely tunable high-Q RF resonator
• Self-detection of motion via dc current
• Easy driving into nonlinear oscillator regime
• Q(T) is consistent with intrinsic dissipation model
• Application as mass sensor: sensitivity 4.2

u

√

Hz

• Without driving: mechanical thermal occupation n ≃ 1.2
• “Large-scale phenomena” of the system – but stay tuned for more!
• A. K. H¨

uttel et al., NanoLett. ASAP (2009), doi:10.1021/nl900612h