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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

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slide1

Review of Mesoscopic Thermal Transport Measurements

Li Shi

IBM Research

&

University of Texas at Austin

IMECE01, New York, November 12, 2001

outline
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

1 micro nano devices
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
molecular electronics
Molecular Electronics

Nanotube

Nanowire Arrays

(Lieber et al., Harvard)

TubeFET (McEuen et al.,

Berkeley)

Nanotube Logic (Avouris et al., IBM Research)

length scale

1 mm

Wl: boundary scattering

W  lF: quantized effects

Ll: ballistic transport

-

W

+

-

L

Length Scale

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

slide6

2. Thermal Conductivity: k = ke+ kp

1

3

C ~ T d

lst

k

lst ~ lum

T

kp

=

C

v

l

Phonon mfp

Specific heat

Sound velocity

lum ~eQ/ T

If T > Q, C ~ constant

If T << Q, C ~ T d (d: dimension)

Specific heat :

Mean free path:

lst ~ constant

Static scattering (phonon -- defect, boundary):

Umklapp phonon scattering:

lum ~ eQ/ T

2 1 measurements of thin film thermal conductivity
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

soi thin films
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

anisotropic polymer thin films
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
superlattices

1. Song, Liu, Zeng, Borca-Tasiuc, Chen, Caylor, Sands, Appl. Phys. Lett. 77, 3154 (2000)

Superlattices

2. Huxtable, Majumdar et al., Micro Therm. Eng. (2001)

2 2 1d nanostructure i nanowires
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)

slide12

(ii) Carbon Nanotube

-- Semiconducting or Metallic

Multiwall

-- Metallic

Semiconducting

Metal

l

ic

E

E

10 nm

E

E

F

F

k

k

Super high current

109 A/cm2

Single Wall

microns

1-2 nm

thermal conductivity of nanotubes

~ 200 W/m-K

(Hone et al., 2000)

Previous Measurement of Nanotube Mats:

Nanotube mat

  • Unknown filling factor
  • Thermal resistance at
  • tube- tube junctions
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:

slide14

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

I0 sin(wt)

Electrode

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) evenwhenDT = 0
another 1d method a hybrid nanotube microdevice
Another 1D Method -- A Hybrid Nanotube Microdevice

Multiwall nanotube

Pt heater line

SiNx beam

Pt heater line

Suspended island

device fabrication

(c) Lithography

Device Fabrication

Photoresist

(a) CVD

SiNx

SiO2

(d) RIE etch

Si

(b) Pt lift-off

Pt

(e) HF etch

measurement scheme

Thermal Conductance:

10 nm multiwall tube

VTE

Beam

Thermopower:

Q = VTE/(Th-Ts)

Island

Pt heater line

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

measurements
Measurements

Cryostat: T : 4-350 K

P ~ 10-6 torr

Resistance of the Pt line

Resistance vs. Joule Heat

m

thermal conductivity
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

thermal conductivity20

3000

k(T) (W/m K)

2000

1000

0

100

200

300

T (K)

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

slide21

Thermopower

For metals w/ hole-type majority carriers:

 T

more on 1d measurements

Single Wall Nanotube

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
slide23

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

3 thermal microscopy of micro nano devices

Techniques Spatial Resolution

3. Thermal Microscopy of Micro-Nano Devices

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)

scanning thermal microscope

Thermal

Topographic

Z

T

X

X

Scanning Thermal Microscope

Atomic Force Microscope (AFM) + Thermal Probe

Laser

Deflection

Sensing

Cantilever

Temperature

Sensor

Sample

X-Y-Z

Actuator

thermal probe

Ta

Rc

Rt

Tt

Rts

Ts

Q

Thermal Probe
probe fabrication

Pt

SiO2

SiO2 tip

200 nm

1 mm

Probe Fabrication
microfabricated probes
Microfabricated Probes

Pt Line

Laser Reflector

Tip

Pt-Cr

Junction

SiNx Cantilever

Cr line

10 mm

Shi, Kwon, Miner, Majumdar, J. MicroElectroMechanical Sys., 10, p. 370 (2001)

locating defective vlsi via
Locating 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

calibration

S =

W

R

  • W(mm) S(K/K)
  • 0.56
  • 6 0.46
  • 0.2 0.06
Calibration
tip sample heat transfer

W , air 

  • W = 0.2 mm, Air ~ Solid + Liquid
  • W < 0.1 mm, Air << Solid + Liquid

W

Why saturated?

Tip-Sample Heat Transfer
why g sol saturated
Why GSol Saturated?

Elastic-Plastic Contact of an Asperity and a Plane

What is the thermal conductance at the nano contact?

slide33

Thermal Transport at Nano Contacts

Modeling results:

GLiq ~ 7 nW/K, GSol ~ 0.8 W/m2-K-Pa

L < Mean free path of air or phonon

Shi and Majumdar, J. Heat Transfer, in press

slide34

Thermal Imaging of Nanotubes

Thermal

30

10

10

20

5

5

Height (nm)

Height (nm)

30 nm

30 nm

10

0

0

0

-400

-200

0

200

400

-400

-400

-200

-200

0

0

200

200

400

400

Distance (nm)

Distance (nm)

Multiwall Carbon Nanotube

Topography

Topography

3 V

m

88

A

m

m

1

1

m

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)

slide35

Electron Transport in Nanotube

Ballistic (Frank et al., 1998)

Diffusive (Bachtold et al., 2000)

Multiwall

Single Wall Semiconducting

Diffusive (McEuen et al., 2000)

Ballistic at low bias (Bachtold ,et al.)

Diffusive at high bias (Yao et al., 2000)

Single Wall Metallic

Ballistic (long mfp)

Diffusive (short mfp)

-

-

+

+

-

-

mfp: electron mean free path

slide36

Dissipation in Nanotube

Nanotube

Electrode

bulk

Electrode

Junction

Diffusive – Bulk Dissipation

T

T profile 

diffusive or ballistic

X

Ballistic – Junction Dissipation

T

X

slide37

Multiwall Nanotube

Thermal

Topographic

DTtip

A

B

3 K

1 mm

0

  • Diffusive at low and high biases

B

A

A

B

metallic single wall nanotube

Low bias: ballistic

contact dissipation

High bias: diffusive

bulk dissipation

Metallic Single Wall Nanotube

Optical phonon

Topographic

Thermal

DTtip

A

B

C

D

2 K

0

1 mm

semiconducting single wall nanotube

Thermal

DTtip

A

B

2 K

Bulk heating at low and

high biases  diffusive

0

Semiconducting Single Wall Nanotube

Topographic

1 mm

Nanotube field-effect transistor

Contact

Nanotube

Vs

Vd = gnd

SiO2

Si Gate

Vg

more on thermal microscopy
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
summary

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