Ronggui Yang, Associate Professor
S.P. Chip and Lori Johnson Faculty Fellow
Department of Mechanical Engineering
Materials Science and Engineering Program
University of Colorado, Boulder, CO 80309
Tel: (303) 735-1003, Fax: (303) 492-3498
Email: Ronggui.Yang@Colorado.Edu
http://spot.colorado.edu/~yangr

1. Introduction to Nanoscale Heat Conduction
2. Transient Thermoreflectance Measurement of Thermal Properties in Thin Films
- Thermal Conductivity vs. Heat Capacity
- Anisotropic Thermal Conductivity: Cross-Plane vs. In-Plane
3. Measurement of Phonon Mean Free Path using Ultrafast EUV Probes
- Quasi-Ballistic Phonon Transport and Average Phonon Mean Free Path
- Collectively-Diffusive Phonon Transport and Mean Free Path Spectroscopy

Courtesy of Professor Kenneth Goodson’s interpretation of DARPA’s Thermal Management
Technologies and ICECool program led by Dr. Avi Bar-Cohen and Dr. Tom Kenny

COLD SIDE
Gate
Source
Channel
Drain
HOT SIDE
MOSFET Laser Diode Energy Conversion

10
5
10
4
10
3
10
2
PHONON (Si)
ELECTRON (Au)
AIR MOLECULE k
=
1
3
Cv Λ carriers electrons phonons photons air molecules wavelength
10-100 nm
1 nm
0.1-10
µ m
0.01 nm
10
1
0 50 100 150 200 250 300
TEMPERATURE (K)
Λ
~ 300 nm, τ ~ 100 ps in silicon at room temperature
G. Chen, D. Borca-Tascuic and R.G. Yang, “Nanoscale Heat Transfer,” in “Encyclopedia of Nanoscience and Nanotechnology”, edited by H.S. Nalwa, Vol. 7, pp. 429-459, American Scientific Publishers, 2004

Silicon Thin Films
Silicon-Germanium Superlattices
K.L. Wang, UCLA
S. Pei, Houston in,BULK c,BULK
Marconnet, Asheghi, and Goodson, J. Heat Transfer, 2013 c,FILM
EXPERIMENTAL in,FILM BULK ALLOY (300K) p=0.6
p=0.5
Lines – Fitting with Chen’s Model p=0.6
120 160 200 240 280
G. Chen, Physical Review B, 1998

Single Wall Carbon Nanotube (CNT)
Theory
Berber, et al, Physical Review Letters 84 4613 (2000)
Experiment
Kim, et al, Applied Physics Letters 87, 215502 (2001)
Pop et al, MRS Bulletin, 37(1273), 2012

Thermal Interface Materials
Thermoelectric Materials
Courtesy of Dr.Avi Bar-Cohen from DARPA
Zhao, Dravid, and Kanatzidis, Energy and Environmental Science, Vol. 7, pp. 251-267, 2014

10 -10 10 -9 10 -8 10 -7 10 -6 10 -5
First
Principles Molecular
Dynamics
Boltzmann-Transport-Equationbased Simulations
10 -4 10 -3
Continuum Theory
10 -2
Transient Thermoreflectance (FDTR & TDTR) Micro-Device-Based Metrology Scanning Probe-Based Metrology

1. Introduction to Nanoscale Heat Conduction
2. Transient Thermoreflectance Measurement of Thermal Properties in Thin Films
- Thermal Conductivity vs. Heat Capacity
(K,C)=(1.35, 1.62)
- Anisotropic Thermal Conductivity: Cross-Plane vs. In-Plane
3. Measurement of Phonon Mean Free Path using Ultrafast EUV Probes
- Quasi-Ballistic Phonon Transport and Average Phonon Mean Free Path
- Collectively-Diffusive Phonon Transport and Mean Free Path Spectroscopy

Transient Thermoreflectance Method For
Thermal Properties of Nanostructured Materials
Pump film substrate
Detector
∆
∆
T
( ) max
≈
∆
∆
R
( ) max
Probe
Sub-ps Pulse laser
Mechanical stage
Sample
Pump
Detector
Modulator
Function generator
Lock-in
Amplifier
J. Zhu, et al, Journal of Applied Physics, Vol. 108, Art # 094315, 2010.
J. Liu, et al, Review of Scientific Instruments, Vol. 84 , Art # 034902, 2013.

Pump beam intensity
12.5ns
1000ns 150fs time
Sample surface temperature
Experiment data time
Delay time t
1
Probe beam intensity
Best fit curve
(K,C)
Delay time (ns)
Thermoreflectance time time

Heat capacity C is usually the input for extracting thermal conductivity K.
Al metal film
Differential Scanning Calorimeter (DSC) can be used for materials in bulk forms
A new material
Si substrate
Bulk form of new material might not be available
Heat capacity input limits the accuracy of thermal conductivity measurement!
Typically only cross-plane thermal properties are measured.
K r
K z
Beam spot size: 10-20 µm
Thermal diffusion length: ~100 nm- 1 µm
One-dimensional heat transfer: K z
, G
Graphite
K z
K r
AlAs
GaAs
AlAs/GaAs Superlattice

Frequency-Dependent TDTR Method for Simultaneous
Measurement of Thermal Conductivity and Heat Capacity
Thermal Penetration Depth: L
=
2 D film
ω
Modulation Frequency
L
2
L
1 Semi-infinite
Low frequency modulation
Experiment data
High frequency modulation
Low frequency: Thermal diffusivity
K
C
K
Best fit curve with (K, C) pairs
(K,C)
Delay time (ns)
High Frequency: Thermal effusivity KC
C
J. Liu, et al, Review of Scientific Instruments, Vol. 84, Art # 034902, 2013.

2
(K,C)=(1.35, 1.62)
J. Liu, et al, Review of Scientific
Instruments, Vol. 84, Art # 034902, 2013.

Atomic/Molecular Layer-Deposited (ALD/MLD)
Hybrid Organic-Inorganic Materials
Inorganic Nanolaminate (ALD W/Al
2
O
3
)
S. M. George, Chem. Rev., 110(111),2010.
Interface Density (nm -1 )
R. M. Costescu, et al, Science, 303(989),2004.
Hybrid Organic-Inorganic Crystals, Interfaces and Nanocomposites
MO
3
(L) x
Perovskite-Like Structures ALD/MLD Hybrid Multi-layer Materials metallic organic
Organic-inorganic interfaces
Dependence on backbone stiffness
Thickness-dependence
George SM, Yoon B, Dameron AA. Accounts of Chemical Research. 2009.
Zhang et al, JACS 135, p. 17401-17407, 2013

Type-A
Porous films
Type-B Type-C
Zincone MLD film Zincone MLD film Zincone ALD: MLD film
ZnO crystalline-like
Amorphous-like
K (Al
2
O
3
) =1.23 W/mK
G=66.25 MW/m 2 K
Liu et al, Nano Letters, Vol. 13, p. 5594, 2013

Type-A
Type-B
Type-C
Liu et al, Nano Letters, Vol. 13, p. 5594, 2013 11/20

amorphous-like crystalline-like
Liu et al, Nano Letters, Vol. 13, p. 5594, 2013

1. Introduction to Nanoscale Heat Conduction
2. Transient Thermoreflectance Measurement of Thermal Properties in Thin Films
- Thermal Conductivity vs. Heat Capacity
- Anisotropic Thermal Conductivity: Cross-Plane vs. In-Plane
K z
K r
AlAs
GaAs
Graphite AlAs/GaAs Superlattice
3. Measurement of Phonon Mean Free Path using Ultrafast EUV Probes
- Quasi-Ballistic Phonon Transport and Average Phonon Mean Free Path
- Collectively-Diffusive Phonon Transport and Mean Free Path Spectroscopy

Transient Thermoreflectance for
Anisotropic Thermal Conductivity
Frequency-domain measurement
Scan through a large range of modulation frequency f (0.025
- 20 MHz) using a small beam spot R (2 - 6 um)
Photothermal method
R
R
L r L r1
L r2
L r3
…
L rn
Thermal diffusion length L r
= κ r
/
π
Cf
A. J. Schmidt, et al, Rev. Sci. Instru. 80(094901),2009.
Nonconcentric beams/offset spots
Scan through the sample surface
µ
)
Laser heating x
0 signal
Offset x
0
0
J. P. Feser, et al, Rev. Sci. Instru. 83(104901),2012.

Anisotropic Thermal Conductivity Measurment
- Varying the Beam Spot Sizes
R
Pump beam
Probe beam
Position of Sample Stage
Our approach
Choose one beam spot size R
1 and modulation frequency f
1
R
1
>>
=
L k r r
1
π
Cf
1
Cross-plane thermal properties K z and G
Choose many small beam spots R
2,
…, R n and modulation frequency f
2
( R n
< R
1
, f
2
< f
1
)
R n
~
=
L r 2 k r
π
Cf
2
In-plane thermal conductivity K r

Kr
Al thin film
HOPG Kz
SPI grade II HOPG

R = 13 - 21.3 µm
R =27.2 µm
The measured Kz and Kr (T>250K) agree well with the literature values.
The discrepancy between the measured Kr (T<250K ) and the literature values could be due to the size effect using small beam spots, similar to the observation by Gang Chen’s group for measuring phonon mean free path in silicon [
Phys. Rev. Lett., 107(095901), 2011
] .

Sputtered W
Al
150 - 250 nm sputtered W
2 nm Ti
Glass substrate
Atomic layer deposited (ALD) W
Al
6 - 35 nm ALD W
2 nm alumina
Glass substrate

1. Introduction to Nanoscale Heat Conduction
2. Transient Thermoreflectance Measurement of Thermal Properties in Thin Films
- Thermal Conductivity vs. Heat Capacity
- Anisotropic Thermal Conductivity: Cross-Plane vs. In-Plane
3. Measurement of Phonon Mean Free Path using Ultrafast EUV Probes
- Quasi-Ballistic Phonon Transport and Average Phonon Mean Free Path
- Collectively-Diffusive Phonon Transport and Mean Free Path Spectroscopy

Kn=L/MFP = 1.0
Ge
Electrons
Mean Free Path Λ =1-50 nm
Wavelength λ =1-50 nm
1 0
5
1 0
4
Λ
λ
Phonons
=10-300 nm
=1 -5nm
P H O N O N ( S i)
E L E C T R O N ( A u )
A IR M O L E C U L E
1 0
3 k
=
1
3
Cv Λ
Si
Temperature
Kn=L/MFP= 25.0
1 0
2
1 0
1
0 5 0 1 0 0 1 5 0 2 0 0
T E M P E R A T U R E (K )
2 5 0 3 0 0
Temperature
But how to measure phonon mean free path?
Nano-Si in Ge matrix
R.G. Yang, and G. Chen, Physical Review B, Vol. 69, 195316, 2004

r
T
1
1 r
2
T
2
r
2
>> r
1
Diffusive Limit
Q
F
=
4k
π r
1
(
T
1
−
T
2
)
=
4
3
Cv
Λ π r
1
(
T
1
−
T
2
)
Ballistic Limit
Q
R
= π r
2
Cv ( T
1 , e
−
T
2
)
≈
2
π r
2
Cv
(
T
1
−
T
2
)
Chen, Journal of Heat Transfer, Vol. 118, pp. 539-545, 1996
Siemens, et al, Nature Materials, Vol. 9, pp. 26-30, 2010

p
Fused silica or
Sample:
L from 2 µm - 65 nm h=20 nm, η =L/p= 0.25
Siemens, et al, Nature Materials, Vol. 9, pp. 26-30, 2010

p
Signal components:
• Decay:
Heat flow from nanostructure
• Oscillation:
Surface acoustic wave propagation
Siemens, et al, Nature Materials, Vol. 9, pp. 26-30, 2010
31

Ni on Fused Silica substrate
Ni on Sapphire substrate
• Fused silica substrate:
Λ ~2 nm
• Sapphire substrate:
Λ ~120 nm
Siemens, et al, Nature Materials, Vol. 9, pp. 26-30, 2010
L
L
Λ ~
Λ ~ 2 nm
32

1. Introduction to Nanoscale Heat Conduction
2. Transient Thermoreflectance Measurement of Thermal Properties in Thin Films
- Thermal Conductivity vs. Heat Capacity
- Anisotropic Thermal Conductivity: Cross-Plane vs. In-Plane
3. Measurement of Phonon Mean Free Path using Ultrafast EUV Probes
- Quasi-Ballistic Phonon Transport and Average Phonon Mean Free Path
- Collectively-Diffusive Phonon Transport and Mean Free Path Spectroscopy

First-Principles Simulation of
Phonon Transport and Thermal Properties
Phonon Dispersion
20
Silicon example
DFT
Tersoff
Exp.
16
12
8
4
0
Γ
K X
Γ
Phonon Relaxation Time
10000
1000
TA1
TA2
LA
LO
TO1
TO2
100
10
1
0.5
1 2 4
Frequency (THz)
8 16
L
Lucas Lindsay, David Broido, Natalio Mingo, 2007-
K. Esfarjani, G. Chen, and H.T. Stokes, Phys. Rev. B, Vol. 84, # 085204, 2011.

Phonon Mean Free Path Spectroscopy inspired by our Nature Materials 2010
Gang Chen’s Group, Physical Review Letters, Vol. 107, #095901, 2011 Jonathan Malen’s Group, Nature Communications, 2013 doi:10.1038/ncomms2630

( /Λ) = tanh
2Λ
( /Λ) = 1 − tanh
2Λ http://arxiv.org/abs/1407.0658

Ultrafast Characterization Meets Quantum Mechanics Simulations http://arxiv.org/abs/1407.0658

4000
2000
Bins used for fit of r eff
MFP most suppressed by given L and P=4L
800
600
400
200
Experimental
Configurations
0
0 200 400 600 800 1000 4000 http://arxiv.org/abs/1407.0658

1.
Nanoscale heat conduction plays an important role in modern information and energy systems.
Fundamental research, both theoretically and experimentally, are needed for better understanding of nanoscale thermal transport mechanisms.
2.
Pump-and-probe method using femto-second lasers is essential for nanoscale thermal transport measurement. We demonstrated simultaneous measurement of thermal conductivity and heat capacity in both bulk and thin film materials using frequency-dependent time-domain transient thermoreflectance (TDTR) signals and measurement of anisotropic thermal conductivity by varying beam spot sizes of transient thermoreflective measurement.
3.
Ultrafast shortwave length extreme ultraviolet (EUV) and soft x-ray lasers are extremely powerful in measuring surface deformation. By using metallic nano-grating, new regimes of nanoscale thermal transport (collectively-diffusive, quasi-ballistic, and diffusive) were identified. High resolution phonon mean free path spectroscopy was developed using EUV light.

Nano-enabled Energy Conversion, Storage, and Thermal Management Systems (NEXT)
• Energy Conversion: Thermoelectrics, Photovoltaics, & Light Emitting Diodes
• Thermal Management: Phase-Change Heat Transfer, Thermal Interface Materials, & Thermoelectrics
• Energy Storage: Lithium Ion Batteries, & Thermal Energy Storage
Advanced Characterization
• Solid-Solid and Solid-Liquid
Thermal Interfaces
• Ultrafast Laser-Based Thermal
Characterization
Nanostructured Materials and
Devices
• Physics-Based Design
• Cost-Effective Manufacturing
Multi-scale and Multi-physics Modeling and Simulations:
Quantum Mechanics/Molecular Dynamics, Nonequilibrium Green’s
Function, Boltzmann Transport Equation (Monte Carlo, Finite
Element/Difference Methods), Simplified Physical Models.

Femtosecond Laser-based Pump-and-Probe System for
Nanoscale Heat Conduction
Some NanoManufacturing Facilities
Phase-Change Heat Transfer Characterization Facilities
Pool Boiling with High Speed
Visualization
Spray Loop (Boiling,
Evaporation and Jet), at NREL
Low-temperature CVD growth
Scalable manufacturing of porous alumina templates
Flow Boiling Loop
CU-Boulder for NGAS Innovation Day,
Condensation Loop 4/16/2014
CHI Electrochemical
Workstation
41