Title: Review of Mesoscopic Thermal Transport Measurements
1Review of Mesoscopic Thermal Transport
Measurements
Li Shi IBM Research University of Texas at
Austin IMECE01, New York, November 12, 2001
2Outline
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
31. 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
4Molecular Electronics
Nanotube
Nanowire Arrays (Lieber et al., Harvard)
TubeFET (McEuen et al., Berkeley)
Nanotube Logic (Avouris et al., IBM Research)
5Length 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
62. 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
72.1 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
8SOI 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
9Anisotropic 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
10Superlattices
1. Song, Liu, Zeng, Borca-Tasiuc, Chen, Caylor,
Sands, Appl. Phys. Lett. 77, 3154 (2000)
2. Huxtable, Majumdar et al., Micro Therm. Eng.
(2001)
112.2 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)
12(ii) Carbon Nanotube
Super high current 109 A/cm2
Single Wall
microns
1-2 nm
13Thermal 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
14The 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
15Another 1D Method -- A Hybrid Nanotube
Microdevice
Multiwall nanotube
Pt heater line
SiNx beam
Pt heater line
Suspended island
16Device Fabrication
(c) Lithography
Photoresist
(a) CVD
SiNx
SiO2
(d) RIE etch
Si
(b) Pt lift-off
Pt
(e) HF etch
17Measurement 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
18Measurements
Cryostat T 4-350 K P 10-6
torr
Resistance of the Pt line
Resistance vs. Joule Heat
m
19Thermal 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
20Thermal 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
21Thermopower
For metals w/ hole-type majority carriers
? T
22More 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
232.3 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
243. 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)
25Scanning Thermal Microscope
Atomic Force Microscope (AFM) Thermal
Probe
Laser
Deflection Sensing
Cantilever
Temperature Sensor
Sample
X-Y-Z Actuator
26Thermal Probe
27Probe Fabrication
28Microfabricated 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)
29Locating Defective VLSI Via
Tip Temperature Rise (K)
Topography
19
21
40 mA
Via
Metal 1
23
28
25
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
30Calibration
31Tip-Sample Heat Transfer
32Why GSol Saturated?
Elastic-Plastic Contact of an Asperity and a Plane
What is the thermal conductance at the nano
contact?
33Thermal 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
34Thermal 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)
35Electron Transport in Nanotube
Ballistic (long mfp)
Diffusive (short mfp)
-
-
-
-
mfp electron mean free path
36Dissipation in Nanotube
Nanotube
Electrode
bulk
Electrode
Junction
Diffusive Bulk Dissipation
T
T profile ? diffusive or ballistic
X
Ballistic Junction Dissipation
T
X
37Multiwall Nanotube
Thermal
Topographic
DTtip
A
B
3 K
1 mm
0
- Diffusive at low and high biases
B
A
A
B
38Metallic Single Wall Nanotube
Optical phonon
Topographic
Thermal
DTtip
A
B
C
D
2 K
0
1 mm
39 Semiconducting Single Wall Nanotube
Topographic
1 mm
Nanotube field-effect transistor
Contact
Nanotube
Vs
Vd gnd
SiO2
Si Gate
Vg
40More 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
41Summary
- 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