Ultrafast laser-based metrology for micron-scale measurements of thermal transport, coefficient of

thermal expansion, and temperature

David G. Cahill,Xuan Zheng, Chang-Ki Min, Ji-Yong Park

Materials Research Lab and Department of Materials Science, U. of Illinois

J.-C. Zhao

Department of Materials Science and Engineering, The Ohio State University

supported by DOE and ONR

Time domain thermoreflectance since 2003

• Improved optical design• Normalization by out-of-

phase signal eliminates artifacts, increases dynamic range and improves sensitivity

• Exact analytical model for Gaussian beams and arbitrary layered geometries

• One-laser/two-color approach tolerates diffuse scattering

Clone built at Fraunhofer Institute for Physical Measurement, Jan. 7-8 2008

psec acoustics andtime-domain thermoreflectance

• Optical constants and reflectivity depend on strain and temperature

• Strain echoes give acoustic properties or film thickness

• Thermoreflectance gives thermal properties

Time-domain Thermoreflectance (TDTR) data for TiN/SiO2/Si

• reflectivity of a metal depends on temperature

• one free parameter: the “effective” thermal conductivity of the thermally grown SiO2 layer (interfaces not modeled separately)

SiO2

TiN

Si

Windows software

author: Catalin Chiritescu, users.mrl.uiuc.edu/cahill/tcdata/tdtr_m.zip

TDTR: Flexible, convenient, and accurate

• ...with 3 micron resolution…

Thermal conductivity map of a human tooth

www.enchantedlearning.com/ Distance from the DEJ (μm)

-400 -200 0 200

ΛC

/C0

(W m

-1 K

-1)

0.0

0.5

1.0

1.5

2.0

dentin enamel

100 μm

High throughput data using diffusion couples

SEM (backscattered)

thermal conductivity

Mapping of a metallurgical diffusion couple

Carbon nanotubes

• Evidence for the highest thermal conductivity any material (higher conductivity than diamond)

Yu et al. (2005)

Maruyama (2007)

Can we make use of this?

• Much work world-wide:

– thermal interface materials

– so-called "nanofluids" (suspensions in liquids)

– polymer composites and coatings

Fischer (2007)

Lehman (2005)

Thermal conductivity and interface thermal conductance

• Thermal conductance (per unit area) G is a property of an interface

• Thermal conductivity Λ is a property of the continuum

Nanotubes in surfactant in water: Transient absorption

• Optical absorption depends on temperature of the nanotube

• Assume heat capacity is comparable to graphite

• Cooling rate (RC time constant) gives interface conductance

G = 12 MW m-2 K-1

Nanotubes in surfactant in water

Critical aspect ratio for a fiber composite

• Isotropic fiber composite with high conductivity fibers (and infinite interface conductance)

• But this conductivity if obtained only if the aspect ratio of the fiber is high

Critical aspect ratio of a fiber composite

• Troubling question: Did we measure the relevant value of the conductance?

"heat capacity G" vs. "heat conduction G"

nanotube/alkane

W/Al2O3

Au/water

PMMA/Al2O3

Interface thermal conductance: Factor of 60 range at room temperature

L = Λ/GΛ = 1 W m-1 K-1

Time-domain probe beam deflection (TD-PBD) for CTE measurements

θProbe

Sample

Al (~100 nm)

Bi-cell photodiode

Lock-inamplifier

V(t) = Vin(t) + iVout(t)

t (ps)0 2000 4000

Vin

/Vou

t

-1

0

1

2

3

4

spatial resolution ~ laser spot size (~ 4 μm)

Model for the beam deflection

Al

Thermal expansion of Al film

Substrate

Bi-axial stressof Al film

Substrate

g g

Thermal expansion and bi-axial stress

of substrate

Substrate

Z3

L ≈ 100 nm

dzTZ AlAlT

L

Al

Al,01 1

1 αυυ

∫ −+

= ∫=L

AlAlTAl dzTBg0 ,α

U

UYUY

ρυυυ

=

⋅∇∇−+

+∇+

)()21)(1(2

2)1(2

Z2

UT

UYUY

ρυυυ

+∇=

⋅∇∇−+

+∇+

)()21)(1(2

2)1(2

Model for the beam defection (continued)

Al

)exp(11

0 φirikniknr =++−+

=

r

rφ

airZSurfTempZZZZZ ++++= 321

Al

Temperature gradienton surface

Heated air

πλφ4dT

dsurfaceTpSurfaceTemZ =

dzairTdTdn

airZ ∫ ∞−=

02

Validation of CTE measurements

t (ps)0 2000 4000

Vin

/Vou

t

-1

0

1

2

3

4

Al(100 nm)/Si

Accepted CTE (10-6 K-1)

1 10 100

Mea

sure

d C

TE (1

0-6

K-1

)1

10

100

ZnMg

AlMn

SnCaF2

Cu

NiCo

SrTiO3Ti

RhZr

CrSi

Invar

SiO2

Accuracy: ±6%

Ni35Fe65

CTE of Fe-Ni diffusion couple

Position (μm)0 200 400 600 800

CTE

(10-

6 K

-1)

0

4

8

12

16

Ni c

once

ntra

tion

(at.%

)

020406080

100

SEM Fe Ni

Ni concentration (at.%)0 20 40 60 80 100

CTE

(10-

6 K

-1)

0

4

8

12

16

Guillaume

Present experiment

Use ion bombardment to reduce atomic short range order

Ni concentration (at.%)25 30 35 40 45 50

CTE

(10-

6 K

-1)

0

4

8

12

16

Before ion bombardment

0.01 dpa

0.03 dpa

0.1 dpa

Ion Dose (dpa)0.00 0.05 0.10

CTE

(10-

6 K

-1)

0

1

2

3

4

5

Fe65Ni35

Er:fiber-laser pump-probe system at UIUC

Transient absorption below the band gap of Si

• Pump-probe measurements of two-photon absorption

• Ф is the normalized absorption

pump

probe

Si wafer

λ=1.55 μm

Two-photon (+one phonon) absorption is strongly temperature dependent

• 470 cm-1 (670 K) phonon population controls the optical absorption

• Simple calibration based on well-known physics

Thermometry by two-photon absorption

• Volume probed is 6×6×50 μm3

• Sensitivity is < 1 K in a 1 kHz bandwidth

Control of Heat Transfer at Interfaces

Conclusions

• Time domain thermoreflectance (TDTR) is now a robust and routine method for measuring the thermal conductivity of almost anything (that has a smooth surface).

• Difficult to take advantage of superlative properties of carbon nanotubes because of "thermally weak" interfaces.

• Time domain probe beam deflection (TD-PBD) provides micron-scale measurements of coefficient of thermal expansion

• Transient absorption by below band-gap (1.56 μm) two-photon absorption provides a fast, spatially resolved thermometer in Si