Micro-Nano Thermal-Fluid:
Physics, Sensors, Measurements
Cantilever Sensors:
An Example of what you will learn in ME 381R
Prof. Li Shi
Micro-Nano Thermal-Fluid Laboratory
Department of Mechanical Engineering
The University of Texas at Austin
lishi@mail.utexas.edu
Outline
• Cantilever Thermal Sensors:
Thermal Property of Nanotubes and Nanowires
• Cantilever Thermal Sensors:
Scanning Thermal Microscopy
• Cantilever Bio Sensors
• Cantilever IR Sensors
2
Silicon Nanoelectronics
Gate
Source
Drain
Nanowire Channel
Courtesy: C. Hu et al., Berkeley
3
Length Scale
Size of a Microprocessor
MEMS Devices
Lattice vibration
1 mm
Thin Film Thickness in ICs
100 nm
10 nm
Nanowire Diameter
l (Phonon
mean free
path at RT)
1 nm
Atom
W  l: boundary scattering
-
1Å
W -
+
L
4
Thermal Conductivity
k = 13 C v l
Specific heat
Mean free path:
Phonon Mean Free path
Sound velocity
1 1 1
 
l lst lum
Umklapp phonon scattering
Static scattering (phonon -- defect, boundary)
5
Silicon Nanowires
Increased boundary scattering  Suppressed thermal conductivity
Thermal Conductivity (W/m-K)
 Localized hot spots
Bulk Si: k ~150 W/m-K
60
Diameter:
50
115nm
40
30
56nm
20
30nm
10
0
0
Li, et al.
40
80
120
160
200
Temperature (K)
240
280
320
360
6
Thermoelectric Nanowires
Thermoelectric Figure of Merit: ZT = S2Ts / k
TE Cooler
Hot I
N
P
Bi or Bi2Te3 nanowires (Dresselhaus et al., MIT):
Cold
Top View
Al2O3 template
Smaller d, shorter boundary scattering mfp
 Lowered thermal conductivity k = Cvl/3
 High ZT, high COP
7
Carbon Nanotubes
Super high current
109 A/cm2
Single Wall -- Semiconducting or Metallic
microns
Multiwall -- Metallic
1-2 nm
8
Thermal Conductivity of Nanotubes
• Strong SP2 bonding (high v), few scattering (long l)  high k
• Theory: 3000 ~ 6000 W/m-K at RT (e.g. Berber et al., 2000)
9
A Cantilever Sensor for Thermal Sensing of Nano- Wires/Tubes
Suspended SiNx Membrane
Long SiNx Cantilever
Pt Resistance Heater/Thermometer
10
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
14 nm multiwall tube
VTE
Beam
Island
Pt heater line
Thermopower:
Q = VTE/(Th-Ts)
11
Device Fabrication
(c) Lithography
Photoresist
(a) CVD SiN
x
SiO2
(d) RIE etch
Si
(b) Pt lift-off
Pt
(e) HF etch
12
14 nm multiwall tube
Thermal Conductivity (W/m-K)
Thermal Conductivity
3500
3000
2500
2000
~T2
1500
l ~ 0.5 mm
1000
500
0
0
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 ~ 0.5 mm
13
Kim, Shi, Majumdar, McEuen, Phy. Rev. Lett 87, 215502-1 (2001)
400
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
14
Single Wall Carbon Nanotubes
Nanotube
15
Bi2Te3 Nanowire
High-efficiency refrigerators!
16
Outline
• Cantilever Thermal Sensors:
Thermal Property of Nanotubes and Nanowires
• Cantilever Thermal Sensors:
Scanning Thermal Microscopy
• Cantilever Bio Sensors
• Cantilever IR Sensors
17
Molecular Electronics
Nanotube Interconnect
(Dai et al., Stanford)
TubeFET (McEuen et al., Berkeley)
Nanotube Logic (Avouris et al., IBM)
18
Electron Transport in Nanotubes
Ballistic (long mfp)
+
Diffusive (short mfp)
+
mfp: electron mean free path
Ballistic (Frank et al., 1998)
Multiwall Diffusive (Bachtold et al., 2000)
Ballistic at low bias (Bachtold ,et al.)
Single Wall Metallic Diffusive at high bias (Yao et al., 2000)
19
Dissipation in Nanotubes
Electrode
Nanotube
bulk
Electrode
Junction
Diffusive – Bulk Dissipation
T
X
T profile 
diffusive or ballistic
Ballistic – Junction Dissipation
T
X
20
Thermal Microscopy
Techniques
Spatial Resolution
Infrared Thermometry
1-10 mm*
Laser Surface Reflectance
1 mm*
Raman Spectroscopy
1 mm*
Liquid Crystals
1 mm*
Near-Field Optical Thermometry
< 1mm
Scanning Thermal Microscopy (SThM)
< 100 nm
*Diffraction limit for far-field optics
21
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
22
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
23
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
24
Microfabricated Probes
Pt Line
Pt-Cr
Junction
Tip
Laser Reflector
SiNx Cantilever
10 mm
Cr Line
Shi, Kwon, Miner, Majumdar, J. MicroElectroMechanical Sys.,
10, p. 370 (2001)
25
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) 26
Via
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)
27
Shi, Kim, et al.
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)
28
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
29
Outline
• Cantilever Thermal Sensors:
Thermal Property of Nanotubes and Nanowires
• Cantilever Thermal Sensors:
Scanning Thermal Microscopy
• Cantilever Bio Sensors
• Cantilever IR Sensors
30
Detecting Biomolecules
Conventional: Fluorescence
New: Micro-cantilever
probes
~500 mm
A B
add sample
deflection
• Surface stress 
wash,
add marker,
wash
• Fewer steps
• Label - free
31
Chemo-mechanical database: PSA
•
Prostate-specific antigen (PSA)
•
Important levels are ~1-10 ng/mL (30-300 pM)
80
Wu et al, Nature Biotech. 19, 856-860 (2001).
2
 [mJ/m ]
60
40
20
0
-20
0.001
0.1
10
1000
100000
fPSA concentration [ng/mL]
•
32
 ~ 5 - 10 mJ/m2, independent of cantilever geometry.
Multiplexing
Why?
CCD
Throughput
Differential Signal
Molecular Profile
A B
N lasers,
• 1 laser
N detectors.
• 1 detector
33
Outline
• Cantilever Thermal Sensors:
Thermal Property of Nanotubes and Nanowires
• Cantilever Thermal Sensors:
Scanning Thermal Microscopy
• Cantilever Bio Sensors
• Cantilever IR Sensors (See PowerPoint File 2)
34