Review of Mesoscopic Thermal Transport Measurements

1
Review of Mesoscopic Thermal Transport
Measurements
Li Shi IBM Research University of Texas at
Austin IMECE01, New York, November 12, 2001
2
Outline
1. Thermal Transport in Micro-Nano Devices 2.
Thermal Property Measurements of Low-Dimensional
Structures -- 2D Thin Films --
1D Nanotubes, Nanowires -- Quantized Thermal
Conductance 3. Thermal Microscopy of Micro-Nano
Devices
3
1. Micro-Nano Devices
MEMS/NEMS Bio Chip (Wu et al., Berkeley)
Microelectronics Si FET (Hu et al., Berkeley)
Gate
Drain
Source
Nanowire Channel

• Consisting of 2D and/or 1D structures

4
Molecular Electronics
Nanotube
Nanowire Arrays (Lieber et al., Harvard)
TubeFET (McEuen et al., Berkeley)
Nanotube Logic (Avouris et al., IBM Research)
5
Length Scale
1 mm
Size of a Microprocessor
MEMS Devices
1 mm
Thin Film Thickness in ICs
100 nm
l (Mean free path at RT)
10 nm
Nanotube/ Nanowire Diameter
1 nm
lF (Fermi wavelength)
Atom
1 Å
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2. Thermal Conductivity k ke kp
kp

C
v
l
Phonon mfp
Specific heat
Sound velocity
lum eQ/ T
If T gt Q, C constant If T ltlt Q, C
T d (d dimension)
Specific heat
Mean free path
lst constant
Static scattering (phonon -- defect, boundary)
lum eQ/ T
Umklapp phonon scattering
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2.1 Measurements of Thin-Film Thermal Conductivity
The 3w method -- Cahill, Rev. Sci. Instrum. 61,
802 (1990)
Metal line
Thin Film

• I 1w
• T I2 2w
• R T 2w
• V IR 3w

L
2b
V
I0 sin(wt)
Si Substrate
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SOI Thin Films

• Ashegi, Leung, Wong, Goodson, Appl. Phys. Lett.
  71, 1798 (1997)
• 2. Ju and Goodson, Appl. Phys. Lett. 74, 3005
  (1999)

Courtesy of Ref. 2
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Anisotropic Polymer Thin Films
Ju, Kurabayashi, Goodson, Thin Solid Films 339,
160 (1999)

• By comparing temperature rise of the metal line
  for different line
• width, the anisotropic thermal conductivity can
  be deduced

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Superlattices
1. Song, Liu, Zeng, Borca-Tasiuc, Chen, Caylor,
Sands, Appl. Phys. Lett. 77, 3154 (2000)
2. Huxtable, Majumdar et al., Micro Therm. Eng.
(2001)
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2.2 1D Nanostructure (i) Nanowires

• Si Nanowires for Electronic Applications
• Bi Nanowires for TE Cooling (Dresselhaus et al.,
  MIT)

Top View
Al2O3 template

• Boundary scattering modified phonon
  dispersion (group velocity)
• ? Suppressed thermal conductivity

Volz and Chen, Appl. Phys. Lett. 75, 2065 (1999)
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(ii) Carbon Nanotube
Super high current 109 A/cm2
Single Wall
microns
1-2 nm
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Thermal Conductivity of Nanotubes
high v, long l ? high k
Carbon Nanotube
3000 6000 W/m-K at room temperature (e.g.
Berber et al., 2000)
Theoretical Expectation
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The 3w method for 1D Structures
-- Lu, Yi, Zhang, Rev. Sci. Instrum. 72, 2996
(2001)

• Low frequency V(3w) 1/k
• High frequency V(3w) 1/C
• Tested for a 20 mm dia. Pt wire
• Results for a bundle of MW nanotubes
• C linear T dependence, low k 100 W/mK

V
Electrode
I0 sin(wt)
Wire
Substrate

• 3w Mechanism DT V2/k and R Ro aDT
• Applicable to an individual SW nanotube?
• -- R4p Rjunction Rbulk
• -- Rjunction ? Rjunction,0 aDT
• -- Rbulk Rbulk (V) even when DT 0

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Another 1D Method -- A Hybrid Nanotube
Microdevice
Multiwall nanotube
Pt heater line
SiNx beam
Pt heater line
Suspended island
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Device Fabrication
(c) Lithography
Photoresist
(a) CVD
SiNx
SiO2
(d) RIE etch
Si
(b) Pt lift-off
Pt
(e) HF etch
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Measurement Scheme

Gt kA/L



T

T

T

s
s
h

Q
I
R


t
R
R

h

h
h
s
T
u
be


Q

IR

l
l
Environment

I
T

0
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Measurements
Cryostat T 4-350 K P 10-6
torr
Resistance of the Pt line
Resistance vs. Joule Heat
m
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Thermal Conductivity
? T2
l 0.5 mm
14 nm multiwall tube

• Room temperature thermal conductivity 3000
  W/m-K
• k T2 Quasi 2D graphene behavior at low
  temperatures
• Umklapp scattering 320 K , l 500 nm
• Nearly ballistic phonon transport

Kim, Shi, Majumdar, McEuen, Phy. Rev. Lett, in
press
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Thermal Conductivity
Interlayer phonon mode filled 2D
14 nm individual MW tube
2.0
80 nm bundle
Junctions in bundles reduce k and lst
2.5
Interlayer phonon mode unfilled 3D
200 nm bundle
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Thermopower
For metals w/ hole-type majority carriers
? T
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More on 1D Measurements

• Short lst and suppressed k found for Si
  nanowires (D. Li et al.)
• Bi and Bi2Te3 wires to be measured
• Challenges of measuring single wall nanotube

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2.3 Quantized Thermal Conductance
Electron thermal conductance quantization
(Molenkamp et al., 1991)
Quantum point contact
Phonon thermal conductance quantization (Schwab
et al., 1999)
Quantum of Thermal Conductance
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3. Thermal Microscopy of Micro-Nano Devices
Techniques
Spatial Resolution
Infrared Thermometry
1-10 mm Laser Surface Reflectance 1
1 mm Raman Spectroscopy
1 mm Liquid Crystals
1 mm Near-Field Optical
Thermometry 2 lt 1 mm Scanning Thermal
Microscopy (SThM) lt 100 nm
Diffraction limit for far-field optics 1. Ju
Goodson, J. Heat Transfer 120, 306 (1998) 2.
Goodson Asheghi, Microscale Thermophysical Eng.
11, 225 (1997)
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Scanning Thermal Microscope
Atomic Force Microscope (AFM) Thermal
Probe
Laser
Deflection Sensing
Cantilever
Temperature Sensor
Sample
X-Y-Z Actuator
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Thermal Probe
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Probe Fabrication
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Microfabricated Probes
Pt Line
Laser Reflector
Tip
Pt-Cr Junction
SiNx Cantilever

Cr line
10 mm

Shi, Kwon, Miner, Majumdar, J. MicroElectroMechani
cal Sys., 10, p. 370 (2001)
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Locating Defective VLSI Via
Tip Temperature Rise (K)
Topography
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21
40 mA
Via
Metal 1
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28
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Metal 2
20 mm
Cross Section
Passivation

• Collaboration TI
• Shi et al., Int. Reli. Phys.
• Sym., p. 394 (2000)

Metal 2
Dielectric
0.4 mm Via
Metal 1
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Calibration
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Tip-Sample Heat Transfer
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Why GSol Saturated?
Elastic-Plastic Contact of an Asperity and a Plane
What is the thermal conductance at the nano
contact?
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Thermal Transport at Nano Contacts
Modeling results GLiq 7 nW/K, GSol 0.8
W/m2-K-Pa
L lt Mean free path of air or phonon
Shi and Majumdar, J. Heat Transfer, in press
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Thermal Imaging of Nanotubes
Multiwall Carbon Nanotube
Topography
Topography
3 V
m
88
A
m
m
1
m
1
m
Spatial Resolution
V)
m
30 nm
50 nm
50 nm
Thermal signal (
Distance (nm)
Shi, Plyosunov, Bachtold, McEuen, Majumdar, Appl.
Phys. Lett., 77, p. 4295 (2000)
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Electron Transport in Nanotube
Ballistic (long mfp)
Diffusive (short mfp)
-
-


-
-
mfp electron mean free path
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Dissipation in Nanotube
Nanotube

Electrode
bulk

Electrode


Junction

Diffusive Bulk Dissipation
T
T profile ? diffusive or ballistic
X
Ballistic Junction Dissipation
T
X
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Multiwall Nanotube
Thermal
Topographic
DTtip
A
B
3 K
1 mm
0

• Diffusive at low and high biases

B
A
A
B
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Metallic Single Wall Nanotube
Optical phonon
Topographic
Thermal
DTtip
A
B
C
D
2 K
0
1 mm
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Semiconducting Single Wall Nanotube
Topographic
1 mm
Nanotube field-effect transistor
Contact
Nanotube
Vs
Vd gnd
SiO2
Si Gate
Vg
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More on Thermal Microscopy

• UHV and low-temperature thermal and
  thermoelectric microscopy
• Near-field radiation and solid conduction
  through a point contact, e.g. in
  thermally-assisted magnetic writing and
  thermomechanical data storage

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Summary

• Nanotube Thermal Conductivity
• --Majumdar, McEuen

• Thin film Thermal Conductivity
• --Cahill, Goodson, Chen, Majumdar

L
2b
V
I0 sin(wt)

• Thermal Conductance Quantum
• --Roukes

• Thermal Microscopy of Nanotubes
• -- Majumdar