Document 7369054
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Transcript Document 7369054
Review of Mesoscopic Thermal
Transport Measurements
Li Shi
IBM Research
&
University of Texas at Austin
IMECE01, New York, November 12, 2001
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
2
1. Micro-Nano Devices
Microelectronics
MEMS/NEMS
Bio Chip (Wu et al., Berkeley)
Si FET (Hu et al., Berkeley)
Gate
Drain
Source
Nanowire Channel
• Consisting of 2D and/or 1D structures
3
Molecular Electronics
Nanotube
Nanowire Arrays
(Lieber et al., Harvard)
TubeFET (McEuen et al.,
Berkeley)
Nanotube Logic (Avouris et 4al.,
IBM Research)
1 mm
Length Scale
Size of a Microprocessor
MEMS Devices
1 mm
Thin Film Thickness in ICs
100 nm
10 nm
Nanotube/ Nanowire Diameter
W lF: quantized effects
L l: ballistic transport
1 nm l (Fermi
F
1Å
wavelength)
Atom
W l: boundary scattering
-
l (Mean free
path at RT)
W -
+
L
5
2. Thermal Conductivity: k = ke + kp
kp= 13 C v l
Specific heat
Phonon mfp
Sound velocity
If T > Q,
Specific heat :
If T << Q,
k
lst
C ~Td
C ~ constant
lst ~ lum
C ~ T d (d: dimension)
lum ~ eQ/ T
T
1 1 1
Mean free path:
l lst lum
Static scattering (phonon -- defect, boundary): lst ~
constant
Q
/
T
Umklapp phonon scattering: lum ~ e
6
2.1 Measurements of Thin-Film Thermal Conductivity
The 3w method -- Cahill, Rev. Sci. Instrum. 61, 802 (1990)
Metal line
L
Thin Film
2b
V
I0 sin(wt)
• I ~ 1w
• T ~ I2 ~ 2w
• R ~ T ~ 2w
• V~ IR ~3w
Si Substrate
P 1 Ds
1
i
Pd
T (2w )
ln 2 ln2w
Lk s 2 b
2
4 2 Lbk f
7
SOI Thin Films
1. Ashegi, Leung, Wong, Goodson, Appl. Phys. Lett. 71, 1798 (1997)
2. Ju and Goodson, Appl. Phys. Lett. 74, 3005 (1999)
Courtesy of Ref. 2
8
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
9
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)
10
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)
11
(ii) Carbon Nanotube
Super high current
109 A/cm2
Single Wall -- Semiconducting or Metallic
microns
1-2 nm
Multiwall -- Metallic
E
Semiconducting
EF
E
Metallic
EF
k
k
12
Thermal Conductivity of Nanotubes
Carbon Nanotube: high v, long l high k
3000 ~ 6000 W/m-K at room temperature
Theoretical Expectation: (e.g. Berber et al., 2000)
Previous Measurement of Nanotube Mats: ~ 200 W/m-K
(Hone et al., 2000)
Nanotube mat
• Unknown filling factor
• Thermal resistance at
tube- tube junctions
13
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
V
Wire
I0 sin(wt)
• Tested for a 20 mm dia. Pt wire
Electrode
Substrate
• Results for a bundle of MW nanotubes:
C ~ linear T dependence, low k ~ 100 W/mK
• 3w Mechanism: T~ V2/k and R ~ Ro + aT
• Applicable to an individual SW nanotube?
-- R4p = Rjunction + Rbulk
-- Rjunction Rjunction,0 + aT
-- Rbulk ~ Rbulk (V) even when T = 0
14
Another 1D Method
-- A Hybrid Nanotube Microdevice
Multiwall nanotube
Pt heater line
SiNx beam
Pt heater line
Suspended island
15
Device Fabrication
(c) Lithography
Photoresist
(a) CVD SiN
x
SiO2
(d) RIE etch
Si
(b) Pt lift-off
Pt
(e) HF etch
16
Measurement Scheme
Gt = kA/L
Thermal Conductance:
Ts
Th
Qh=IRh
Rh
Qh Ql Ts T0
Gt
Th Ts 2T0 Th Ts Ql=IRl
I
t
Tube
Ts
Rs
Environment
T0
10 nm multiwall tube
VTE
Beam
Island
Pt heater line
Thermopower:
Q = VTE/(Th-Ts)
17
Cryostat: T : 4-350 K
P ~ 10-6 torr
Resistance (k )
Measurements
6
4
Resistance of the Pt line
2
0
0
Resistance vs. Joule Heat
m
100
200
300
Temperature (K)
18
k (103 W/m K)
Thermal Conductivity
T2
3
2
l ~ 0.5 mm
1
0
14 nm multiwall tube
100
200
300
Temperature (K)
• 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
19
Thermal
Conductivity
-7
Interlayer phonon
mode filled – 2D
14 nm individual
MW tube
-8
10
2.0
3000
k(T) (W/m K)
Thermal Conductance (W/K)
10
-9
10
80 nm
bundle
2000
Junctions in bundles
reduce k and lst
1000
2.5
Interlayer phonon
mode unfilled – 3D
0
2
10
3
4
5
100
200
300
T (K)
200 nm bundle
6 7 8 9
100
Temperature (K)
2
3
4
20
Thermopower (mV/K)
Thermopower
100 For metals w/ hole-type majority carriers:
80
Q
2 k B 2T
6eE F
60
40
Ts
20
T
0
50
100
150
200
Temperature (K)
250
300
21
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
Single Wall Nanotube
22
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
23
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]
< 1 mm
Scanning Thermal Microscopy (SThM)
< 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)
24
Scanning Thermal Microscope
Atomic Force Microscope (AFM) + Thermal Probe
Laser
Deflection
Sensing
Cantilever
Temperature
Sensor
Z Topographic
X
Sample
X-Y-Z
Actuator
Thermal
T
X
25
Thermal Probe
Ta
Cantilever
Mount
Cantilever
Rc
Tip
Rt
Tt
Rts
Ts
Substrate
Sample
Solid-Solid
Conduction
Pt
Liquid-Film
Conduction
SiO2
Cr
Liquid
Air Conduction
Radiation
Sample
Q
26
Probe Fabrication
Cr
SiO2
SiO2
SiO2 tip
Pt
Si
SiNx
100~500 nm
Photoresist
1 mm
Photoresist
Cr
Pt
Pt
SiO2
SiO2
Pt
RIE+HF Etch
Cr
200 nm
27
Microfabricated Probes
Pt Line
Pt-Cr
Junction
Tip
Laser Reflector
SiNx Cantilever
Cr line
10 mm
Shi, Kwon, Miner, Majumdar, J. MicroElectroMechanical Sys.,
10, p. 370 (2001)
28
Locating Defective VLSI Via
Tip Temperature Rise (K)
Topography
19
21
Via
Metal 1
28
25
20 mm
Cross Section
Passivation
Metal 2
Dielectric
Metal 1
23
• Collaboration: TI
0.4 mm • Shi et al., Int. Reli. Phys.
Sym., p. 394 (2000) 29
Via
Topography
Thermal
0
Au
line
10
8
I
S = 0.46 K/K
6
W
4
2
Lead
0
R
5
10
22 mm 20
15
Sample temperature rise (K)40
W(mm) S(K/K)
50
0.56
6
0.46
0.2
0.06
0.1
20
0
0
2
4
6
X (mm)
8
10
0
2
4
6
X (mm)
8
0.0
10
30
T (au)
0
Height (nm)
Junction temperature rise (K)
Calibration
Tip-Sample Heat Transfer
•W , air
•W = 0.2 mm, Air ~ Solid + Liquid
W
•W < 0.1 mm, Air << Solid + Liquid
0.06
Approaching
0
Solid
Retracting
0.04
-100
Liquid
0.02
Air
-200
Why saturated?
0.1
0.2
Temperature response (K/K)
Jump to contact
Snapped out
of contact
100
Deflection (nm)
0.08
0.00
0.3
Sample vertical position (mm)
0.4
31
Why GSol Saturated?
Elastic-Plastic Contact of an Asperity and a Plane
Tip end
90 nm
10 nm
Liquid
Sample
Asperity
What is the thermal conductance at the nano contact?
32
Temperature response (K/K)
Thermal Transport at Nano Contacts
Modeling results:
GLiq ~ 7 nW/K, GSol ~ 0.8 W/m2-K-Pa
0.06
Model
L < Mean free path of
air orfitphonon
Measured
Solid
0.04
Liquid
0.02
0.00
0.1
Air
0.2
0.3
0.4
Sample vertical position (mm)
Shi and Majumdar, J. Heat Transfer, in press
33
Thermal Imaging of Nanotubes
Multiwall Carbon Nanotube
Topography
Thermal
3V
88 mA
1 mm
Height (nm)
10
30
nm
30 nm
5
0
-400
-200
0
200
Distance (nm)
400
Thermal signal ( m V)
Spatial Resolution
30
20
50 nm
nm
50
10
0
-400
-200
0
200
400
Distance (nm)
Shi, Plyosunov, Bachtold, McEuen, Majumdar,
Appl. Phys. Lett., 77, p. 4295 (2000)
34
Electron Transport in Nanotube
Ballistic (long mfp)
+
Diffusive (short mfp)
+
mfp: electron mean free path
Ballistic (Frank et al., 1998)
Multiwall Diffusive (Bachtold et al., 2000)
Single Wall Semiconducting Diffusive (McEuen et al., 2000)
Ballistic at low bias (Bachtold ,et al.)
Single Wall Metallic Diffusive at high bias (Yao et al., 2000)
E
Low Bias
E
High Bias
Short mfp
Long mfp
k
Acoustic
Phonon
Optical
Phonon
35
k
Dissipation in Nanotube
Electrode
Nanotube
bulk
Electrode
Junction
Diffusive – Bulk Dissipation
T
X
T profile
diffusive or ballistic
Ballistic – Junction Dissipation
T
X
36
Multiwall Nanotube
Topographic
Thermal
B
A
Ttip
3K
1 mm
0
20
•Diffusive at low and high biases
0
B
A
-20
-40
Ttip (K)
Current (mA)
40
20
A
10
B
0
-1000
0
1000
Bias voltage (mV)
0
1
2
Distance (mm)
37
Current (mA)
Metallic Single Wall Nanotube
20
Optical phonon
0
A
B C
D
-20
-2000
-1000
0
1000
2000
Low bias: ballistic
contact dissipation
High bias: diffusive
bulk dissipation
Bias voltage (mV)
Topographic
Thermal
A
B
C
D
Ttip
2K
1 mm
0
38
Semiconducting Single Wall Nanotube
Topographic
A
Thermal
B
Ttip
2K
Bulk heating at low and
high biases diffusive
Nanotube field-effect transistor
Contact
Nanotube
Vs
Vd = gnd
SiO2
Si Gate
Vg
0
Current (mA)
1 mm
10
A
5
0
-5
B
2
5
1
Vg
0 -9
-1000
0
1000
Bias voltage (mV) 39
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
40
• Nanotube Thermal Conductivity
--Majumdar, McEuen
Summary
• Thin film Thermal Conductivity
--Cahill, Goodson, Chen, Majumdar
L
2b
V
I0 sin(wt)
• Thermal Conductance Quantum
--Roukes
• Thermal Microscopy of Nanotubes
-- Majumdar
41