Interface effects on thermophysical properties in nanomaterial systems
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Interface effects on thermophysical properties in nanomaterial systems. Patrick E. Hopkins MAE Dept. Seminar March 22, 2007. Moore’s Law. Rocket nozzle 10 7 W/m 2. Nuclear reactor 10 6 W/m 2. hot plate 10 5 W/m 2. Equivalent power density [W/m 2 ]. 45 nm. 100 nm. 500 nm.

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Interface effects on thermophysical properties in nanomaterial systems

Interface effects on thermophysical properties in nanomaterial systems

Patrick E. Hopkins

MAE Dept. Seminar

March 22, 2007


Moore s law
Moore’s Law nanomaterial systems

Rocket nozzle

107 W/m2

Nuclear reactor

106 W/m2

hot plate

105 W/m2

Equivalent power density [W/m2]

45 nm

100 nm

500 nm

Transistor size


Thermal boundary conductance
Thermal boundary conductance nanomaterial systems

Superlattices

Field effect transistors

Heat

generated

Rejected heat

Thermal management is highly dependent on the boundary of two materials


Today s talk
Today’s Talk nanomaterial systems

Purpose:Determine the effects that the properties of the interface have on thermal boundary conductance, hBD

  • Theory of phonon interfacial transport

  • Measurement of hBD with the TTR technique

  • Influence of atomic mixing on hBD

  • Influence of high temperatures (T > qD) on hBD


Thermal conduction in bulk materials

T nanomaterial systems

Thermal conduction in bulk materials

Thermal conduction

Microscopic picture

L

Z

l = Mean free path [m]

phonon-phonon scattering length in homogeneous material

k = thermal conductivity [Wm-1K-1]

= thermal flux [Wm-2]

What happens if l is on the order of L?


Thermal conduction in nanomaterials

T nanomaterial systems

Z

Thermal conduction in nanomaterials

Microscopic picture of nanocomposite

T

Z

< ln

Ln

keffective of nanocomposite does not depend on phonon scattering in the individual materials but on phonon scattering at the interfaces

hBD = Thermal boundary conductance [Wm-2K-1]

Change in material properties gives rise to hBD


Particle theory of h bd
Particle theory of nanomaterial systemshBD

Phonon flux transmitted across interface

Phonon distribution

Phonon

interfacial transmission

Projects phonon transport perpendicular to interface

Spectral phonon density of states

[s m-3]

Phonon

Energy

[J]

Phonon

speed

[m s-1]


Diffuse scattering
Diffuse scattering nanomaterial systems

  • Scattering completely diffuse

  • Elastically isotropic materials

  • Single phonon elastic scattering

Diffuse Mismatch Model (DMM)

E. T. Swartz and R. O. Pohl, 1989, "Thermal boundary resistance,“ Reviews of Modern Physics, 61, 605-668.

diffuse scattering – phonon “looses memory” when scattered

T > 50 K and realistic interfaces

Averaged properties in different crystallographic directions

Is this assumption valid?


Single phonon elastic scattering events
Single phonon elastic scattering events nanomaterial systems

Simplifies transmission coefficient


Single phonon elastic scattering events1
Single phonon elastic scattering events nanomaterial systems

hBD from DMM limited by f1

f=T/qD

f

Linear in classical regime (T>qD)

*Kittel, 1996, Fig. 5-1


Single phonon elastic scattering
Single phonon elastic scattering nanomaterial systems

Elastic Scattering – hBD is a function of df/dT

Df/dT


Today s talk1
Today’s Talk nanomaterial systems

Purpose:Determine the effects that the properties of the interface has on thermal boundary conductance, hBD

  • Theory of phonon interfacial transport

  • Measurement of hBD with the TTR technique

  • Influence of atomic mixing on hBD

  • Influence of high temperatures (T > qD) on hBD


Transient thermoreflectance ttr

Verdi V10 nanomaterial systems

= 532 nm 10 W

RegA 9000

tp ~ 190 fs

single shot - 250 kHz

4 mJ/pulse

Mira 900

tp ~ 190 fs @ 76 MHz

l = 720-880 nm

16 nJ/pulse

Verdi V5

= 532 nm 5 W

Transient ThermoReflectance (TTR)

Probe Beam

l/2 plate

Beam Splitter

Delay ~ 1500 ps

Sample

dovetail prism

lenses

Polarizer

Detector

Pump Beam

Variable

ND Filter

Acousto-Optic

Modulator

Lock-in Amplifier

Automated Data

Acquisition System


Transient thermoreflectance ttr1

PROBE nanomaterial systems

HEATING

“PUMP”

FILM

Thermal Diffusion

SUBSTRATE

Transient ThermoReflectance (TTR)

Free Electrons Absorb Laser Radiation

Electron-Phonon

Coupling (~2 ps)

Electrons Transfer

Energy to the Lattice

Thermal Diffusion

by Hot Electrons

Thermal Equilibrium

Thermal Diffusion within Thin Film

Thermal Diffusion (~100 ps)

Thermal Conductance across the

Film/Substrate Interface

Thermal Boundary (~2 ns)

Conductance

Substrate Thermal Diffusion (~100 ps – 100 ns)

Thermal Diffusion within Substrate


Thermal model
Thermal Model nanomaterial systems

Nondimensionalized

Temperature

Boundary conditions

Initial conditions


Dmm compared to experimental data
DMM compared to experimental data nanomaterial systems

Goal: investigate the over- and under-predictive trends of the DMM based on the single phonon elastic scattering assumption

Ref 8. Stevens, Smith, and Norris, JHT, 2005

Ref 63. Lyeo and Cahill, PRB, 2006

Ref 65. Stoner and Maris, PRB, 1993


Today s talk2
Today’s Talk nanomaterial systems

Purpose:Determine the effects that the properties of the interface has on thermal boundary conductance, hBD

  • Theory of phonon interfacial transport

  • Measurement of hBD with the TTR technique

  • Influence of atomic mixing on hBD

  • Influence of high temperatures (T > qD) on hBD


Dmm assumptions
DMM Assumptions nanomaterial systems

DMM Assumption

Realistic interface


Sample fabrication
Sample Fabrication nanomaterial systems


Interface characterization
Interface Characterization nanomaterial systems

Auger electron spectroscopy (AES)

Relaxation and

Auger emission

Ionization

Electron bombardment

Monitor energy

e- [3 keV]

Vacuum Energy

Higher levels

Core level


Aes depth profiling
AES Depth Profiling nanomaterial systems

detector

e- gun

O2

Ar+ gun

C

Cr

dN/dE

Si

Energy [eV]


Aes depth profile
AES Depth Profile nanomaterial systems


Aes depth profiles
AES Depth Profiles nanomaterial systems

Cr/Si mixing layer

9.5 nm

Cr-1: no backsputter

Si change

9.7 %/nm

Elemental Fraction

Cr/Si mixing layer

14.8 nm

Cr-2: backsputter

Si change

16.4 %/nm

Depth under Surface [nm]

Hopkins, and Norris, APL, 2006


Results from aes data
Results from AES Data nanomaterial systems


Ttr testing
TTR Testing nanomaterial systems


H bd results
h nanomaterial systemsBD Results

DMM predicts a constant hBD = 855 MWm-2K-1


Virtual crystal dmm
Virtual Crystal DMM nanomaterial systems

Multiple scattering events from interatomic mixing

Beechem, Graham, Hopkins, and Norris, APL, 2006


Vcdmm
VCDMM nanomaterial systems

Hopkins, and Norris, Beechem, and Graham, JHT, Submitted


Summary
Summary nanomaterial systems

  • DMM predicts hBD850 MWm-2K-1 at room temperature

  • Measured data varies from 1-2x108

  • Multiple phonon elastic scattering could cause discrepancy

  • DMM only takes into account single scattering event

  • DMM assumes perfect interface

  • Virtual Crystal DMM predicts same values and trends

    • for Cr/Si at room temperature


Today s talk3
Today’s Talk nanomaterial systems

Purpose:Determine the effects that the properties of the interface has on thermal boundary conductance, hBD

  • Theory of phonon interfacial transport

  • Measurement of hBD with the TTR technique

  • Influence of atomic mixing on hBD

  • Influence of high temperatures (T > qD) on hBD


Single phonon elastic scattering1
Single phonon elastic scattering nanomaterial systems

Elastic Scattering – hBD is a function of df/dT


Molecular dynamics simulations
Molecular Dynamics Simulations nanomaterial systems

Stevens, Zhigilei, and Norris, IJHMT, Accepted


Mismatched samples
Mismatched samples nanomaterial systems

Lyeo and Cahill, PRB, 2006

Stoner and Maris, PRB, 1993


Ttr testing1
TTR Testing nanomaterial systems


H bd results1
h nanomaterial systemsBD results

Hopkins, Salaway, Stevens, and Norris, IJT, 2007

Ref 65. Stoner and Maris, PRB, 1993


H bd results2
h nanomaterial systemsBD results

Hopkins, Stevens, and Norris, JHT, 2007


Analysis
Analysis nanomaterial systems

  • Linear trend in MDS in classical regime

  • MDS calculates hBD with out assuming only elastic scattering in interfacial phonon transport

  • Several samples show linear hBD trends around classical regime

DMM

JOINT FREQUENCY DMM


Jfdmm
JFDMM nanomaterial systems


Dmm vs jfdmm
DMM vs. JFDMM nanomaterial systems


Dmm vs jfdmm1
DMM vs. JFDMM nanomaterial systems


Summary1
Summary nanomaterial systems

  • Inelastic scattering – DMM does not account for this

  • Data at solid-solid interfaces taken at temperatures around Debye Temperature show linear trend

  • DMM predicts flattening of predicted hBDaround Debye Temperature

  • Accounting for substrate phonon population in DMM improves prediction (JFDMM)


Conclusions acknowledgments
Conclusions & Acknowledgments nanomaterial systems

Purpose:Determine the effects that the properties of the interface have on thermal boundary conductance, hBD

  • Realistic interfaces – two phase regions, mixing, nonperfect junctions – multiple phonon scattering events that can decrease hBD

  • Inelastic scattering can occur at elevated temperatures (T > qD), increasing hBD

  • Thanks for the financial support from NSF GRFP, VSGC, U.Va. Faculty Senate and Double Hoo, and NSF grant CTS-0536744

  • Dr. Pam Norris, Dr. Samuel Graham, Thomas Beecham

  • Microscale Crew: Rich Salaway, Rob Stevens, Mike Klopf, Jenni Simmons, Thomas Randolph, Jes Sheehan


Resolving tbc with ttr
Resolving TBC with TTR nanomaterial systems

Al/Al2O3 interfaces

kf = 237 Wm-1K-1

hBD = 2.0 x 108 Wm-2K-1

Resolving TBC with TTR

ti

tf


Thermal model1
Thermal Model nanomaterial systems

Lumped capacitance

substrate

T

film

Al/Al2O3 interfaces

kf = 237 Wm-1K-1

hBD = 2.0 x 108 Wm-2K-1

Bi<<1

d =75 nm< 120 nm

Bi = 1

Bi>>1

x


H bd trends vs sample mismatch
h nanomaterial systemsBD trends vs. sample mismatch


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