Stephan Braig

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Electronics and Mechanics with Carbon Nanotubes
C
Stephan Braig Markus Brink Scott Bunch Lisa
Larrimore Ethan Minot Ji-Yong Park David
Roundy Sami Rosenblatt Vera Sazonova Hande
Ustunel Arend van der Zande Yuval Yaish Xinjian
Zhou Jun Zhu Rena Zieve
Support NSF, DARPA, NASA
McEuen, Arias, Brouwer Groups
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Nanotube band structure
semiconducting
metal
B gt 0
large bandgap
metal
semiconducting
k
1.0
G (e2/h)

0
-10
0
10
Vgate (V)
Vgate (V)
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Electron phonon scattering in nanotubes
O. Dubay et al. Phys. Rev. B. 67, 035401 (2003)

• Backscattering processes (energy and momentum
  conservation)

4
Copying work of Jie Liu et al. (Duke)
Parallel Device Fabrication - CVD
Flying catalyst growth (Liu group)
Gas flow
catalyst pads
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Quantum Limits for a SWNT


Landauer Formula
Maximum Conductance
With scattering, imperfect contacts
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Scattering in Metallic Nanotubes
Low Bias Acoustic Phonons
High Bias-optic, z.b phonons
Yao et al. Phys. Rev. Lett.84, 2941 (2000)
Many groups
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Related Work Freitag et al., PRB (00) de Pablo
et al., PRL (02)
Electron-phonon scattering lengths
50nm
V
100nm
200nm
300nm
1?m
L
2?m
Vg
I
d1.8nm, L010?m

• Current not saturating for short channel length.
  
• Linear I-V curve with slope determined by

Park et al., Nano Lett. (04). See also Javey et
al. PRL (04)
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Nanotube band structure and mobility
semiconducting
G (e2/h)
Reported max. mobilities 1,000 - 100,000 cm2/V-s
Vg (V)
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Temperature scaling
Gmax 1/T, mpeak 1/T
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Model Acoustic Phonons
Effective mass
E
Same as Metallic NT
Band Structure Acoustic Phonon Scattering
G. Pennington et al., Phys. Rev. B 68, 045426
(2003) V. Perebeinos et al., Phys. Rev. Lett. 94,
086802 (2005)
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Diameter Dependence
G (4e2/h)
m (103 cm2/V-s)
G increases with d
Vg (V)
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Diameter Dependence
Gmax versus d
mpeak versus d
Gmax d, mpeak d2
Zhou et al., submitted
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Devices near turnoff Disorder/defects
Occasional large defects
Scanned Gate Microscopy (SGM) Bachtold et
al.(2000), Tans et al. (2000)
Electric Force Microscopy (EFM)
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Single-e Freq. Shift Microscopy (e-FSM)
Coulomb charging rings Dot is at center
Brink et al. (unpublished)
400 nm
Semiconducting nanotube near depletion
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Making Suspended Tubes
Etch SiO2 under Tube
Grow tube over trench
SEM Images
Approach Nygard, Cobden, APL, 79, 4216 (2001)
ApproachTombler et al.
Walters et al. APL 74, 3803 (1999)
AFM Image
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Gated Suspended Nanotube
Modify surface to dope unsuspended regions p-type
E
Vg V
EF
p-type
intrinsic
position
I
V
sd
NT
Vg
gate
L
f
B
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Measuring small bandgaps

30
345 kW
20
I (nA)
435 kW

10
T 210 K
0
-3
0
3
Vg
Eg 37 meV t2 0.8
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Strained lattice
Kane and Mele, PRL, 78 1932 (1997)
k
Cones move when lattice is strained Symmetry is
preserved
Before B-field, / k-vectors were
equivalent Clockwise/Anti-clockwise important
cos3f
Heyd et al. PRB 97, 6820 (1997) Yang et al. PRL
85, 154 (2000) Maiti et al. PRL 88, 126805 (2002)
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Strain-Induced bandgap Engineering?
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Strain and Bandgaps Experimental set-up
cantilever with spring constant ktip
V
tip
current preamp
drain
source
Simultaneously Monitor (1) Mech. Response (2)
Electrical Response
suspended tube
Gate
Previous work
Salvetat et al. PRL 82, 944 (1999) Walters et al.
APL 74, 3803 (1999) Tombler et al. Nature 405,
769 (2000)
Hande Ustanel Arias Group
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Strain-Induced Band Gap in a Metallic Tube
e 0
V
I
Vtip
drain
source
e 2
suspended tube
d 3nm
Gate
Strain converts a metallic tube into a
semic. tube !

strain
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Strain-Induced Band Gap in a Metallic Tube
e 0
e 2
d 3nm
strain
Minot et al. PRL (03)
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Magnetic fields and small bandgaps
B
Axial direction
0.8
DR (MW)


0.4
0.0
0
5
10
B (T)
Theory Ajiki and Ando JPSJ 62 1255 (1993)
Subbands shift oppositely with B
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.
K2
Subband degeneracy lifted with field
K1
.
E(k)
.
.
K2
K1
B gt 0
B 0
Ei(k)
0
k
k
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Suspended nanotube quantum dot

0.005
Low bias
x20

G (e2/h)
0.
0.5
0.3
0.4
0.6
Vg (V)
p-type
gap
n-type
x50
Minot et al. Nature (04)
Similar work by Jarillo-Herrero et al. Nature
429, 389 (2004)
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Energy shifts of orbital levels
electrons
400
morb
350
300
Vg (mV)
U Egap
250
0.01
200
holes
0
150
G (e2/h)
0
4
morb
B (T)
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Quantum dot levels Orbital Zeeman Effect
Minot et al., Nature (04)
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Guitar String Vibrations of Nanotubes
Nano Guitar (Craighead Group)
Nanotube Guitar How do you strum it? How do you
hear it?
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CNT Oscillators Previous work

• Poncharal et al., Science 283, 1513 (1999)
• Gao et al., PRL 85, 622 (2000)
• Reulet et al., PRL 85, 2829 (2000)
• Yu et al., International Conference
  IEEE-NANO2001, Maui, 2001
• Williams et al., APL 89, 255202 (2002)
• Purcell et al., PRL 89, 276103 (2002)
• Babic et al., NanoLett. 3, 1577 (2003)
• Williams et al., APL 82, 805 (2003)
• Fennimore et al., Nature 424 (2003)
• Resonators based on MWNT
• f 1 MHz
• Q 150-2000

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Nanotube Electromechanical Mixer
A(w)
Q
1
wo
w
Drive/tune
detect
See also Cleland group
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Nanotube Mechanical Resonances
Sazonova et al. Nature (04)
Q 50
f 55 MHz
f 5 MHz
Q 80
Device 1
Measured many devices
Device 2
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Response Dependence on Driving Amplitude room
Temp.

• Response is linear up to
• dVg 20 mV
• Nonlinear effects
• Drastic change in shape
• Development of hysteresis

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Tunable Vibrational Modes
High Vg Hanging Chain
Low Vg Bucked beam
Simulations Arias Group
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Possible Sources of Low Quality Factor

• Air drag
• Predicted onset of Q degradation due to air from
  1 to 10 torr
• Wang et al., Phys. Rev. E
• Ohmic losses
• Estimated to be negligible
• Residue or clamping losses
• Intrinsic NT losses?

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SWNT Nanomechanical oscillators
400 MHz

• New Results
• Higher modes,
• higher frequencies
• f 400 MHz
• 2. Higher Qs
• at low T.

f
0 MHz
Simulations Arias Group
5 V
0 V
Vg
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Quality Factor Temperature Dependence

• Q increases for lower temperature
• Nonlinearity starts at lower excitation voltages

Qmax gt 800!
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Phonon-Phonon Scattering
TA
RBM
vibration
Radial breathing mode (RBM)
Transverse acoustic mode (TA)
Requires thermal occupancy of phonons!
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Scanned Probe Techniques/ Elec. Phonon Scattering
Tuning NT Band Gaps
Ethan Minot Yuval Yaish Vera Sazonova Sami
Rosenblatt Markus Brink
Vibrating Nanotubes
Xinjian Zhou Jun Zhu Markus Brink Ji-Yong
Park Yuval Yaish Scott Bunch Sami
Rosenblatt Theory Hande Ustunel, Stephan
Braig (Brouwer/Arias)
Vera Sazonova, Yuval Yaish, Rena Zieve, Arend van
der Zande, Ji-Yong Park, Markus Brink, Theory
Hande Ustunel, David Roundy (Arias)