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

Source Drain

Gate

MicroelectronicsSi FET (Hu et al., Berkeley)

MEMS/NEMSBio Chip (Wu et al., Berkeley)

• Consisting of 2D and/or 1D structures

Nanowire Channel

4

Molecular Electronics

Nanowire Arrays(Lieber et al., Harvard)

TubeFET (McEuen et al., Berkeley)

Nanotube Logic (Avouris et al., IBM Research)

Nanotube

5

Length Scale1 mm

1 m

1 nm

MEMS Devices

Size of a Microprocessor

Nanotube/ Nanowire Diameter

100 nml (Mean freepath at RT)

1 ÅAtom F (Fermi

wavelength)

L

W l: boundary scattering

W F: quantized effects

L l: ballistic transport

- +-W

Thin Film Thickness in ICs

10 nm

6

2. Thermal Conductivity: k = ke + kp

lum ~ e/ T

T

k

C ~ T d

lst

lst ~ lum

kp= C v l13

Specific heat Sound velocityPhonon mfp

If T > C ~ constant If T << C ~ T d (d: dimension)

Specific heat :

umst lll111 Mean free path:

lst ~ constantStatic scattering (phonon -- defect, boundary):

lum ~ e/ TUmklapp phonon scattering:

7

2.1 Measurements of Thin-Film Thermal Conductivity

I0 sin(t)

L 2b

Thin Film

Si Substrate

Metal line

f

s

s LbkPdi

b

D

kLP

T24

2ln21

ln21

)2(2

The 3 method -- Cahill, Rev. Sci. Instrum. 61, 802 (1990)

• I ~ 1• T ~ I2 ~ 2• R ~ T ~ 2• V~ IR ~3

V

8

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

9

Anisotropic Polymer Thin Films

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

Ju, Kurabayashi, Goodson, Thin Solid Films 339, 160 (1999)

10

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)

11

2.2 1D Nanostructure: (i) Nanowires

Top View

• Si Nanowires for Electronic Applications

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

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

Single Wall

-- Semiconducting or Metallic

E

k

Metallic E

Semiconducting

k

EF EF

Super high current109 A/cm2

1-2 nmmicrons

Multiwall -- Metallic

10 nm

13

Thermal Conductivity of Nanotubes

Carbon Nanotube: high v, long l high k

Theoretical Expectation:3000 ~ 6000 W/m-K at room temperature(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

14

The 3 method for 1D Structures

• 3 Mechanism: T~ V2/k and R ~ Ro + T

• Applicable to an individual SW nanotube?

-- R4p = Rjunction + Rbulk

-- Rjunction Rjunction,0 + T

-- Rbulk ~ Rbulk (V) even when T = 0

Substrate

Wire Electrode

-- Lu, Yi, Zhang, Rev. Sci. Instrum. 72, 2996 (2001)

• Low frequency: V(3) ~ 1/k

• High frequency: V(3) ~ 1/C

• Tested for a 20 m dia. Pt wire

• Results for a bundle of MW nanotubes:

C ~ linear T dependence, low k ~ 100 W/mK

I0 sin(t)V

15

Another 1D Method -- A Hybrid Nanotube Microdevice

SiNx beam

Pt heater line

Suspended island

Pt heater line

Multiwall nanotube

16

Device Fabrication

Si

SiO2

SiNx

Pt

Photoresist(a) CVD

(b) Pt lift-off

(c) Lithography

(d) RIE etch

(e) HF etch

17

Measurement Scheme

10 nm multiwall tube

Island

Beam

Pt heater line

Th Ts

t Ts

R s

Rh Qh=IRh

Tube

Ql=IRl

Environment

T0 I

Gt = kA/L

sh

s

sh

lht TT

TT

TTT

QQG

0

02

Thermal Conductance:

VTE

Thermopower:Q = VTE/(Th-Ts)

18

Measurements 6

4

2

0

Res

ista

nce

(k

)

3002001000

Temperature (K)

Resistance of the Pt line

0.4

0.2

0

R

/R(%

)

2.01.51.00.50.0

Power(

m

W )

0.6

Rh

Rs

T

(K)

2

1

0

Cryostat: T : 4-350 K P ~ 10-6 torr

Resistance vs. Joule Heat

19

Temperature (K)

k (1

03W

/m K

)

3

2

1

0

300200100

3

2

1

0

300200100

Thermal Conductivity

• 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

l ~ 0.5 m

T2

Kim, Shi, Majumdar, McEuen, Phy. Rev. Lett, in press

14 nm multiwall tube

20

10-9

10-8

10-7

The

rmal

Con

duct

ance

(W

/K)

102 3 4 5 6 7 8 9

1002 3 4

Temperature (K)

(T) (W/m K)

T (K)

3000

2000

1000

0

300200100

Thermal Conductivity

14 nm individual MW tube

80 nm bundle

200 nm bundle

2.5

2.0

Interlayer phonon mode unfilled – 3D

Interlayer phonon mode filled – 2D

Junctions in bundles

reduce k and lst

21

Thermopower100

80

60

40

20

030025020015010050

Ts

Th

erm

opow

er (V

/K)

Temperature (K)

F

B

eETk

Q6

22

For metals w/ hole-type majority carriers:

T

22

More on 1D Measurements

Single Wall Nanotube

• 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

23

2.3 Quantized Thermal ConductanceElectron thermal conductance quantization (Molenkamp et al., 1991)

Quantum point contact

Phonon thermal conductance quantization (Schwab et al., 1999)

Quantum of Thermal Conductance

24

3. Thermal Microscopy of Micro-Nano Devices

Infrared Thermometry 1-10 m*

Laser Surface Reflectance [1] 1 m*

Raman Spectroscopy 1 m*

Liquid Crystals 1 m*

Near-Field Optical Thermometry [2] < 1 m

Scanning Thermal Microscopy (SThM) < 100 nm

Techniques Spatial Resolution

*Diffraction limit for far-field optics

1. Ju & Goodson, J. Heat Transfer 120, 306 (1998)

2. Goodson & Asheghi, Microscale Thermophysical Eng. 11,

225 (1997)

25

X-Y-Z Actuator

Scanning Thermal Microscope

Sample

Temperature Sensor

Laser

Atomic Force Microscope (AFM) + Thermal Probe

CantileverDeflectionSensing

Thermal

X

TTopographic

X

Z

26

Thermal Probe

Tip

Solid-Solid Conduction

Liquid-Film Conduction

Air Conduction

Radiation

Cantilever Cantilever Mount

Liquid

Cr Pt SiO2

Sample

Substrate

Sample

Rts

Rt

Ts

Ta

Tt

Rc

Q

27

Probe Fabrication

1 m

SiO2 tip

Si

SiO2

SiNx

Photoresist Cr

Cr

RIE+HF Etch

200 nm

Pt SiO2

SiO2

Pt

Pt

CrSiO2

Photoresist

Pt

100~500 nm

28

Microfabricated Probes

Pt-Cr Junction

Laser Reflector

SiNx Cantilever Cr line

Pt Line

Tip

m

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

29

Locating Defective VLSI Via

• Collaboration: TI• Shi et al., Int. Reli. Phys. Sym., p. 394 (2000)Metal 1

DielectricMetal 2

Passivation

0.4 m Via

Cross Section

Topography Tip Temperature Rise (K)

20 m

2823

21

19

25

Met

al 2

ViaMetal 1

40 mA

30

X ( m )

0 2 4 6 8 1 0

Hei

gh

t (n

m)

0

2 0

4 0

T o p o g r a p h y T h e r m a l 0

2 2 m

A u l i n e

L e a d

X ( m )

0 2 4 6 8 1 0

T

(au

)

0 . 0

0 . 1

I

Sample temperature rise (K)

0 5 10 15 20

Junc

tion

tem

pera

ture

ris

e (K

)

0

2

4

6

8

10

0.46 K/KS =

R

Calibration

W(m) S(K/K)50 0.566 0.460.2 0.06

W

31

Tip-Sample Heat Transfer

Sample vertical position (m)

0.1 0.2 0.3 0.4

Te

mp

era

ture

re

spo

nse

(K

/K)

0.00

0.02

0.04

0.06

0.08

De

flect

ion

(n

m)

-200

-100

0

100

Approaching

Retracting

Jump to contactSnapped out of contact

Air

Liquid

Solid

W•W , air •W = 0.2 m, Air ~ Solid + Liquid

•W < 0.1 m, Air << Solid + Liquid

Sample vertical position (m)

0.1 0.2 0.3 0.4

Te

mp

era

ture

re

spo

nse

(K

/K)

0.00

0.02

0.04

0.06

0.08

De

flect

ion

(n

m)

-200

-100

0

100

Approaching

Retracting

Jump to contactSnapped out of contact

Air

Liquid

Solid

Why saturated?

32

Why GSol Saturated?

Elastic-Plastic Contact of an Asperity and a Plane

What is the thermal conductance at the nano contact?

33

L < Mean free path of air or phonon

Sample vertical position (m)0.1 0.2 0.3 0.4T

em

pe

ratu

re r

esp

on

se (

K/K

)

0.00

0.02

0.04

0.06

MeasuredModel fit

Liquid

Air

Solid

Modeling results:

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

Thermal Transport at Nano Contacts

Shi and Majumdar, J. Heat Transfer, in press

34

Thermal Imaging of Nanotubes Multiwall Carbon Nanotube

1 m

Topography

1 m

Topography

3 V88 A

Distance (nm)

Th

erm

al s

ign

al ( V

) 30

20

10

0

4002000-200-400

50 nm

Distance (nm)

Hei

ght

(nm

)

30 nm

10

5

0

4002000-200-400

Distance (nm)

Hei

ght

(nm

)

30 nm

10

5

0

4002000-200-400

Thermal

30 nm 50 nm

Shi, Plyosunov, Bachtold, McEuen, Majumdar, Appl. Phys. Lett., 77, p. 4295 (2000)

Spatial Resolution

35

Electron Transport in Nanotube

- +- - +-

Ballistic (long mfp) Diffusive (short mfp)

mfp: electron mean free path

MultiwallBallistic (Frank et al., 1998)Diffusive (Bachtold et al., 2000)

Single Wall Semiconducting Diffusive (McEuen et al., 2000)

Single Wall MetallicBallistic at low bias (Bachtold ,et al.)Diffusive at high bias (Yao et al., 2000)

E

k

Low Bias E

k

High Bias

Optical Phonon Acoustic

Phonon

Long mfp

Short mfp

36

Dissipation in Nanotube

Nanotube bulk Electrode

Electrode

Diffusive – Bulk Dissipation

Ballistic – Junction Dissipation

Junction

X

X

T

T

T profile diffusive or ballistic

37

20

10

0

210

Distance (m)

Tti

p(K

)

-40

-20

0

20

40

10000-1000

Bias voltage (mV)

Cur

rent

(A

)

1 m

Multiwall NanotubeTopographic

Thermal

A B Ttip

3 K

0

•Diffusive at low and high biases

AB A

B

38

Metallic Single Wall Nanotube

-20

0

20

200010000-1000-2000

Bias voltage (mV)

Cu

rren

t (

A)

AB C D

Bias voltage (mV)

Cu

rren

t (

A)

AB C D

Topographic Thermal

1 m

A B C D

Optical phonon Low bias: ballistic

contact dissipation

High bias: diffusive

bulk dissipation

Ttip

2 K

0

39

Semiconducting Single Wall NanotubeTopographic Thermal

Bulk heating at low and high biases diffusive

A BTtip

2 K

0

10

5

0

-5

10000-1000

-901

25

Bias voltage (mV)

Cu

rren

t (

A)

AB

Vg

Nanotube field-effect transistor

Si GateSiO2

Contact Nanotube

Vg

Vs Vd = gnd

1 m

40

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

41

Summary

I0 sin(t)

L 2b V

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

• Nanotube Thermal Conductivity --Majumdar, McEuen

• Thermal Conductance Quantum --Roukes

• Thermal Microscopy of Nanotubes -- Majumdar