Carbon nanotubes as ultra-high quality factor mechanical resonators - - PowerPoint PPT Presentation

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Carbon nanotubes as ultra-high quality factor mechanical resonators - - PowerPoint PPT Presentation

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Carbon nanotubes as ultra-high quality factor mechanical resonators and much more! Andreas K. H uttel Kavli Institute for Nanoscience, Technische Universiteit Delft, Netherlands Institute for Experimental and Applied Physics,

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SLIDE 1

Carbon nanotubes as ultra-high quality factor mechanical resonators — and much more!

Andreas K. H¨ uttel

Kavli Institute for Nanoscience, Technische Universiteit Delft, Netherlands Institute for Experimental and Applied Physics, Universit¨ at Regensburg, Germany

Condensed Matter and Materials Physics (CMMP10) University of Warwick, Coventry, UK 14 December 2010

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SLIDE 2

Carbon nanotubes: a more exciting

(and not so flat) form of carbon

diamond fullerene(C )

60

graphite/graphene nanotube

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SLIDE 3

Mechanical properties of carbon nanotubes

  • stiffer than steel
  • resistant to damage from physical

forces

  • very light
  • Young’s modulus E =

F/A

∆L/L: ECNT ≃ 1.2TPa, Esteel ≃ 0.2TPa

  • Density:

ρCNT ≃ 1.3

g cm3 ,

ρAl ≃ 2.7

g cm3

  • (still) “material of dreams”

http://www.pa.msu.edu/cmp/csc/ntproperties/

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SLIDE 4

Doubly clamped nanotube resonators

nanotube is suspended like a guitar or violin string low mass, high stiffness → high resonance frequency, large quantum effects single clean macromolecule → low dissipation???

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SLIDE 5

Doubly clamped nanotube resonators

800nm

nanotube is suspended like a guitar or violin string low mass, high stiffness → high resonance frequency, large quantum effects single clean macromolecule → low dissipation???

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SLIDE 6

Vibration modes of carbon nanotubes

0.01 0.1 1 10 1 stretching bending RBM 0.1K kB Energy (meV) L (µm)

  • stretching (longitudinal) mode:

hν ∝ L−1

hν = 1100...110µeV,

ν = 270...27GHz

(for 100nm...1µm)

  • bending (transversal) mode:

hν ∝ L−2

hν = 10...0.1µeV,

ν = 2.4GHz...24MHz

(for 100nm...1µm) hν ∝ d, also tension-dependent

bending stretching RBM

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SLIDE 7

Chip fabrication and measurement setup

400 nm ~2cm

A

Vsd Vg

E(t)

VRF

CNT

source drain 800 nm

gate

  • First make chip (Pt electrodes, trench)
  • Then CVD-grow nanotubes across electrodes
  • 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); AKH et al., Nano Lett. 9, 2547 (2009)
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SLIDE 8

Low-temperature transport: Coulomb blockade

dilution refrigerator T 20mK

  • Tunnel barriers between leads and nanotube
  • Low temperature kBT ≪ e2/C: formation of a quantum dot

D S

source dot gate

N el.

drain

Vg VSD I D S

Vg Coulombblockade

D S

Singleelectron tunneling

Vg dI dVsd

Vsd≈0(linearresponseregime)

CB N-1 el. CB N el. CB N+1 el. SET SET SET

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SLIDE 9

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

~2cm

A

Vsd Vg

E(t)

VRF

gate

  • Sharp resonant structure in Idc(ν)
  • Very low driving power required
  • High Q = ν/∆ν

(∆ν = FWHM)

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

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SLIDE 10

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

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

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SLIDE 11

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

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

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SLIDE 12

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

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

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SLIDE 13

Georg Duffing (1861 – 1944) and his oscillator

Duffing differential equation: m¨ x + cx + bx3 = F sinωt

  • Driven mechanical oscillator with

non-linear response

  • Response becomes bistable

→ large or small amplitude

  • Switching between branches

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

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SLIDE 14

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

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

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SLIDE 15

... 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

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

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SLIDE 16

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)

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

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SLIDE 17

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

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

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SLIDE 18

Detailed ν(Vg): with current, 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

  • G. A. Steele, AKH, et al., Science 325, 1103 (2009)
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SLIDE 19

Model for ν(Vg) – part I: “slope and steps”

(MHz) V

g (V)

N holes N-1 holes tension induced by a single elementary charge

  • Electrostatic force between tube and backgate:

Fdot = 1 2 dCg dz

  • Vg − Vdot

2

  • Quantum dot voltage:

Vdot = CgVg + qdot Cdot

,

qdot(qc) = −|e|N(qc), qc = CgVg

  • Overall slope: continuous increase of voltage Vg on gate
  • Steps: discrete change of Vdot (single elementary charges!)
  • G. A. Steele, AKH, et al., Science 325, 1103 (2009)
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SLIDE 20

Model for ν(Vg) – part II: “steps become dips”

139.5 140.0 (MHz)

  • 0.90
  • 0.88
  • 0.90
  • 0.88
  • 0.90
  • 0.88

V

g (V)

V

g (V) g (V)

Vsd = 0.5 mV

sd = 1.5 mV sd = 2.5 mV

V

V V

  • qc = Cg(z)Vg is function of z
  • Electrostatic contribution to spring constant:

kdot = −dFdot dz

= Vg(Vg − Vdot)

cdot

dCg

dz

2

1−|e|dN dqc

  • Always negative, always decreasing frequency
  • G. A. Steele, AKH, et al., Science 325, 1103 (2009)
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SLIDE 21

Also mechanical Q and nonlinearity dominated by current

  • 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

  • G. A. Steele, AKH, et al., Science 325, 1103 (2009)
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SLIDE 22

Interaction-induced nonlinearity 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

The sign of αdot follows the sign of the curvature of kdot.

  • G. A. Steele, AKH, et al., Science 325, 1103 (2009)
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SLIDE 23

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

  • G. A. Steele, AKH, et al., Science 325, 1103 (2009); Usmani et al., PRB 75, 195312 (2007)
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SLIDE 24

What do we have so far?

  • Mechanical resonator, 120MHz ν 360MHz, Q 150000
  • Easy driving into nonlinear oscillator regime
  • Single-electron steps of the resonance frequency
  • Backaction of single electron tunneling on ν, Q, nonlinearity
  • 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

AKH et al., Nano Lett. 9, 2547 (2009); G. A. Steele, AKH, et al., Science 325, 1103 (2009)

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SLIDE 25

Higher frequency (I): higher vibration modes

200 300 f (MHz) Nh+ 500 1000

1000 500 1 2 3 (MHz) f n

  • higher harmonics visible too
  • dc current signal is smaller

(node(s) in nanotube motion, smaller change in total capacitance)

  • at high tension, integer frequency

multiples (expected for a string resonator)

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SLIDE 26

Higher frequency (II): just make it shorter!

:)

  • ngoing work in Delft and Regensburg

:)

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SLIDE 27

Going super

  • Nanotubes can carry supercurrents via

proximity effect

  • Use superconducting electrodes
  • Cooper pair tunneling
  • Nanotube SQUIDs, ac Josephson effect,

intrinsic cooling of the vibration, ...

  • image: example for beautiful

(non-suspended) hybrid device

  • Superconducting support and control

electronics!

images from J. P . Cleuziou et al., Nat. Nano. 1, 53 (2006)

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SLIDE 28

Pitfalls and problems for ultra-clean samples

  • need to first prepare on-chip infrastructure: contacts, gates, trenches, ...
  • then grow nanotubes across the chip with CVD as last step
  • 10min, 900◦C, CH4 and H2: for a metal thin film “as bad as it gets”
  • melting, recrystallization

→ deformation, loss of conductivity

  • hydrogen / carbon storage in metal

→ lowering of superconductor Tc

  • influence of metal on nanotube growth?
  • properties of nanotube–metal contact?
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SLIDE 29

but... it seems to be working

100 200 300 R ( ) Ω 400 0.5 1 1.5 ~2.8K Tc before CVD after CVD 2 2.5 (K) T „hall-bar“ metal film test structure R■=11.4Ω R■=8.0Ω

∼5 day old SEM images from Regensburg

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SLIDE 30

lots of opportunities

  • beam resonator in quantum mechanical ground state
  • transition classical – quantum harmonic oscillator
  • quantum nonlinear resonator properties (many theory predictions!)
  • ...
  • ...
  • ...
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SLIDE 31

Go quantum limit!

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SLIDE 32

The old team at TU Delft

Thanks!

Gary Steele Benoit Witkamp Menno Poot Leo Kouwenhoven Harold Meerwaldt Herre van der Zant

All references are listed at http://www.akhuettel.de/research/publications.php

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SLIDE 33

My new team at Uni Regensburg

Thanks!

?

Daniel Schmid Dominik Preusche Peter Stiller you? Christoph Strunk and everyone else!

All references are listed at http://www.akhuettel.de/research/publications.php