Carbon nanotubes as ultrahigh-Q electromechanical resonators at - - PowerPoint PPT Presentation

Carbon nanotubes as ultrahigh-Q electromechanical 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 18th International Conference on Electronic Properties of Two-Dimensional Systems — Kobe, 2009

Nanotubes as beam resonators — up to now

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

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

• Nanotube as nonlinear circuit element
• RF downmixing at mech. resonance
• Q 2000 — why?
• HF cables to sample: heating, noise
• Contamination during lithography
• Clamping points?

Chip fabrication and measurement setup

400 nm ~2cm

A

Vsd Vg

E(t)

VRF

CNT

source drain 800 nm

gate

• Nanotube CVD-grown above Pt electrodes, across pre-defined trench
• Back gate connected to a gate voltage source Vg
• RF antenna suspended ∼ 2cm above chip
• Dilution refrigerator (T ≃ 20mK)
• Only dc measurement
• G. A. Steele et al., Nature Nanotech. 4, 363 (2009); A. K. H¨

uttel et al., Nano Lett. 9, 2547 (2009)

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., Nano Lett. 9, 2547 (2009)

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., Nano Lett. 9, 2547 (2009)

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

larger |Vg| −

→ increased tension − → higher frequency ν

• A. K. H¨

uttel et al., Nano Lett. 9, 2547 (2009)

Detection mechanism — mechanically induced averaging

• at resonant driving the nanotube

position oscillates

• oscillating Cg

− → fast averaging over I(Vg)

• black line: dc measurement I(Vg)
• red line: this numerically averaged
• blue: difference, effect of averaging
• red points: measured peak amplitude in

I(ν), for different values of Vg

• 5.22 -5.21
• 5.2
• 5.19

Vg (V)

• 0.1

0.1 1 2 I (nA) I (nA) I (nA) Vg

ac,eff

I

• 0.1

0.1

• A. K. H¨

uttel et al., Nano Lett. 9, 2547 (2009)

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., Nano Lett. 9, 2547 (2009)

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., Nano Lett. 9, 2547 (2009)

Detailed ν(Vg): in SET, frequency decreases

8

I (nA)

dc current

• 0.90
• 0.84

139.2 140.0

(MHz) V

g (V)

N holes N-1 holes

RF response

“Coulomb blockade oscillations of mechanical resonance frequency” electrostatic contribution to spring constant

Also Q and nonlinearity dominated by backaction

• 4.345
• 4.335

V

g (V) 1 nA

α < 0 α > 0 α < 0

• 4.345
• 4.335

256 258 (MHz)

g (V)

ΔIsd

sd (nA) 0.1

• 0.1

ΔIsd (nA) 1.0

• 0.5
• 60 dB

256 258 (MHz)

• 0 (kHz)
• 200

200

Up Down 57000 20000 2900 90000 Q ~

Fit f0

ΔI V

• 45 dB
• Dissipation whenever

charge can fluctuate

• Q decreases on SET

peaks

• Nonlinearity dominated

by tunneling

• Switches between

weakening and softening spring

Summary, conclusion & outlook!

• 120MHz ν 360MHz,

Q 150000

• Self-detection of motion via dc current
• Easy driving into nonlinear oscillator regime
• Q(T) is consistent with intrinsic dissipation model
• Single-electron steps of the resonance frequency
• Backaction of single electron tunneling on ν, Q, nonlinearity
• Self-excitation of motion!
• Estimated motion amplitude at resonant driving ∼ 250pm

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

• Application as mass sensor: sensitivity 4.2

u

√

Hz

• Without driving: mechanical thermal occupation n ≃ 1.2
• Stay tuned for more interesting results!!
• A. K. H¨

uttel et al., Nano Lett. 9, 2547 (2009); G. A. Steele, A. K. H¨ uttel et al.

Self-excitation of the resonator

• 5.19
• 5.17
• 2

2 V

g (V)

V

sd (mV)

A

050 dI/dV ( S)

• 4.935
• 4.93

283.5 284.5 f (MHz)

V

g

V

sd

Isd

5 V

g (V)

Isd (nA)

C D E

V

g

Isd

5

• 4.93
• 0.75

0.5 I

sd (nA)

• 1.05
• 0.95
• 10

10 V

sd (mV)

V

g (V)

B

5

• 10

dI/dV ( S)

10 nA Usmani et al., PRB 75, 195312 (2007)

Model for ν(Vg)

• Electrostatic force between tube and backgate:

Fdot = 1 2 dCg dz

• Vg − Vdot

2

(1)

• Quantum dot voltage:

Vdot = CgVg + qdot Cdot

,

qdot(qc) = −|e|N(qc), qc = CgVg (2)

• Electrostatic contribution to spring constant:

kdot = Vg(Vg − Vdot) cdot

dCg

dz

2

1−|e|dN dqc

• (3)

V

DOT

C

gV g/CDOT

e/C

DOT

qc = C

gV g

1e

• qDOT= |e| N(qc)

qc = C

gV g

Model for α(Vg)

Frequency Gate Voltage α < 0 α < 0 α > 0

αdot = −d3F

dz3 = d2 dz2 kdot(qc) = V 2

g

• dCg

dz

2 d2kdot

dq2

c

(4) The sign of αdot follows the sign of the curvature of kdot.