interface effects on thermophysical properties in nanomaterial systems
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Microscale Heat Transfer Lab – University of Virginia
Interface effects on thermophysical properties in nanomaterial systems
Patrick E. Hopkins
MAE Dept. Seminar
March 22, 2007
Microscale Heat Transfer Lab – University of Virginia
Moore’s Law
hot plate
105 W/m2
Transistor size
Eq
uiv
alen
t p
ow
er d
ensi
ty [
W/m
2]
Nuclear reactor
106 W/m2
500 nm100 nm
45 nm
Rocket nozzle
107 W/m2
Microscale Heat Transfer Lab – University of Virginia
Thermal boundary conductance
k
TSZT
2
SuperlatticesField effect transistors
Heat generated
Rejected heat
Thermal management is highly dependent on the boundary of two materials
Microscale Heat Transfer Lab – University of Virginia
Today’s TalkPurpose: 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 > D) on hBD
Microscale Heat Transfer Lab – University of Virginia
Thermal conduction in bulk materialsThermal conduction
Z
k = thermal conductivity [Wm-1K-1] = thermal flux [Wm-2]
T
qz
Tkqz
z
T
q
= Mean free path [m]
phonon-phonon scattering length in homogeneous material
Microscopic picture
What happens if is on the order of L?
L
Microscale Heat Transfer Lab – University of Virginia
Thermal conduction in nanomaterials
n
Microscopic picture of nanocomposite
Ln
keffective of nanocomposite does not depend on phonon scattering in the individual materials but on phonon scattering at the interfaces Thq BD
T
Z
Z
T
hBD = Thermal boundary conductance [Wm-2K-1]
Change in material properties gives rise to hBD
Microscale Heat Transfer Lab – University of Virginia
Particle theory of hBD
Phonon flux transmitted across interface
ThddjctznDq BDjj
jj
cutoffj
sincos,,,,2
1,1
2/
0 0
,1,1
,1
Spectral phonon density of states[s m-3]
Phonon distribution
Phonon Energy
[J]Phonon
speed[m s-1]
Phonon interfacial transmission
Projects phonon transport perpendicular to interface
Microscale Heat Transfer Lab – University of Virginia
Diffuse scattering
Diffuse Mismatch Model (DMM) E. T. Swartz and R. O. Pohl, 1989, "Thermal boundary resistance,“ Reviews of Modern Physics, 61, 605-668.
j
jjBD
cutoffj
dcTfDT
h,1
0
1,1,11, ,4
1
diffuse scattering – phonon “looses memory” when scattered
• Scattering completely diffuse• Elastically isotropic materials• Single phonon elastic scattering
T > 50 K and realistic interfaces
Averaged properties in different crystallographic directions
Is this assumption valid?
ThddjctznDq BDjj
jj
cutoffj
sincos,,,,2
1,1
2/
0 0
,1,11
,1
Microscale Heat Transfer Lab – University of Virginia
Single phonon elastic scattering events
12,2
2,1
2,2
03,2
2
2
,2
03,1
2
2
,1
03,2
2
2
,2
1,1,1
,1
22
2)(
j jjj
jj
j jj
j jj
j jj
cc
c
dc
cdc
c
dc
c
cutoffj
cutoffj
cutoffj
Simplifies transmission coefficient
21 qq
j
ijijii
cutoffji
dcTfDq,
0
,, ,4
1
3,2
2
2
, 2)(
jji c
D
121 1
Frequency [Hz]
Deb
ye d
ensi
ty o
f Sta
tes
[m-3
]
cutoff1
cutoff2
Microscale Heat Transfer Lab – University of Virginia
Single phonon elastic scattering eventshBD from DMM limited by f1
1exp
1
Tk
f
B
B
cD k
*Kittel, 1996, Fig. 5-1
Linear in classical regime (T>D)
f=T/Df
j
jjBD
cutoffj
dcTfDT
h,1
0
1,1,11, ,4
1
Microscale Heat Transfer Lab – University of Virginia
Single phonon elastic scatteringElastic Scattering – hBD is a function of df/dT
Df/
dT
j
jjBD
cutoffj
dcTfDT
h,1
0
1,1,11, ,4
1
Microscale Heat Transfer Lab – University of Virginia
Today’s TalkPurpose: 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 > D) on hBD
Microscale Heat Transfer Lab – University of Virginia
Transient ThermoReflectance (TTR)Mira 900
p ~ 190 fs @ 76 MHz = 720-880 nm
16 nJ/pulse
Polarizer
Detector
Lock-in AmplifierAutomated Data
Acquisition System
Verdi V5= 532 nm 5 W
RegA 9000
p ~ 190 fssingle shot - 250 kHz
4 J/pulse
Verdi V10= 532 nm 10 W
Probe Beam
Sample
dovetail prism
Delay ~ 1500 ps
lenses
/2 plate Beam Splitter
Acousto-Optic Modulator
VariableND Filter
Pump Beam
Microscale Heat Transfer Lab – University of Virginia
Transient ThermoReflectance (TTR)
SUBSTRATE
FILM
HEATING “PUMP”
PROBE
Thermal Diffusion
Free Electrons Absorb Laser Radiation
Electrons Transfer Energy to the Lattice
Thermal Diffusion by Hot Electrons
Thermal Equilibrium
Thermal Diffusion within Thin Film
Thermal Conductance across the Film/Substrate Interface
Electron-PhononCoupling (~2 ps)
Thermal Diffusion (~100 ps)
Thermal Boundary (~2 ns)Conductance
Thermal Diffusion within Substrate
Substrate Thermal Diffusion (~100 ps – 100 ns)
Microscale Heat Transfer Lab – University of Virginia
Thermal Model
)](),0([)(
ttdC
h
dt
tdfs
f
bdf
2
2 ),(),(
x
tx
t
tx ss
s
Initial conditions Boundary conditions
1)0( f
0)0,( xs
NondimensionalizedTemperature
)],0()([),0(
tthx
tk sfBD
ss
0),(
x
ts
0
0,, )0( TT
TT
f
sfsf
Microscale Heat Transfer Lab – University of Virginia
DMM compared to experimental data
Ref 8. Stevens, Smith, and Norris, JHT, 2005Ref 63. Lyeo and Cahill, PRB, 2006Ref 65. Stoner and Maris, PRB, 1993
Goal: investigate the over- and under-predictive trends of the DMM based on the single phonon
elastic scattering assumption
Microscale Heat Transfer Lab – University of Virginia
Today’s TalkPurpose: 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 > D) on hBD
Microscale Heat Transfer Lab – University of Virginia
DMM Assumptions
DMM Assumption Realistic interface
Microscale Heat Transfer Lab – University of Virginia
Sample FabricationSample
IDBacksputter
EtchHeat Treat Prior
to DepositionDeposition Notes
Cr-1 none none 50 nm Cr @ 300 K
Cr-2 5 min none 50 nm Cr @ 300 K
Cr-3 5 min 20 min @ 873 K 50 nm Cr @ 300 K
Cr-4 5 min 50 min @ 873 K 50 nm Cr @ 300 K
Cr-5 5 min 20 min @ 873 K 50 nm Cr @ 573 K
Cr-6 5 min none 10 nm of Cr at 300 K;Heating to 770 K;40 nm of Cr at 300 K
Microscale Heat Transfer Lab – University of Virginia
Interface CharacterizationAuger electron spectroscopy (AES)
Relaxation andAuger emissionIonizationElectron bombardment
Higher levels
Core level
Vacuum Energy
e- [3 keV]Monitor energy
Microscale Heat Transfer Lab – University of Virginia
AES Depth Profiling
Ar+ gun
e- gundetector
Si
O2
Cr
C
dN
/dE
Energy [eV]
Microscale Heat Transfer Lab – University of Virginia
AES Depth Profile
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60
Depth into film [nm]
Ele
me
nta
l fra
cti
on
Cr/Si mixing regionCr
Si
C
O2
Microscale Heat Transfer Lab – University of Virginia
AES Depth Profiles
0
0.2
0.4
0.6
0.8
1
30 40 50 60
Ele
me
nta
l fr
ac
tio
n
0
0.2
0.4
0.6
0.8
1
30 40 50 60
Ele
me
nta
l fr
ac
tio
n
Cr-1: no backsputter
Cr-2: backsputter
Cr/Si mixing layer9.5 nm
Cr/Si mixing layer14.8 nm
Depth under Surface [nm]
Ele
men
tal F
ract
ion Si change
9.7 %/nm
Si change16.4 %/nm
Hopkins, and Norris, APL, 2006
Microscale Heat Transfer Lab – University of Virginia
Results from AES DataSample
IDCr Film
Thickness [nm]
Mixing Layer[nm]
Slope of Si in Beginning of Mixing
Layer [%/nm]
Cr-1 38 ± 2.1 9.5 ± 0.6 9.7 ± 0.7
Cr-2 37 ± 0.4 14.8 ± 1.0 16.4 ± 0.7
Cr-3 35 ± 0.5 11.5 ± 0.7 16.6 ± 1.0
Cr-4 35 ± 2.8 10.8 ± 0.8 7.4 ± 1.0
Cr-5 39 ± 0.5 5.8 ± 0.5 24.1 ± 1.0
Cr-6 45 ± 0.5 7.0 ± 0.4 28.1 ± 1.2
Microscale Heat Transfer Lab – University of Virginia
TTR Testing
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000 1200 1400
Time [ps]
No
rmal
ized
R
/R
Model fit pointt = 100 ps
Cr-2: h BD = 1.13x108 W m-2 K
Cr-1: h BD = 1.78x108 W m-2 K
Microscale Heat Transfer Lab – University of Virginia
hBD Results
DMM predicts a constant hBD = 855 MWm-2K-1
Microscale Heat Transfer Lab – University of Virginia
Virtual Crystal DMM
VCVCBD RRD
R
2int1intint
int
1
21int
int 111
j
VCj
j
VCjp
BD hh
D
Gkh
BDhR
1int
Beechem, Graham, Hopkins, and Norris, APL, 2006
int
int
D
Multiple scattering events from interatomic mixing
Microscale Heat Transfer Lab – University of Virginia
VCDMM
Hopkins, and Norris, Beechem, and Graham, JHT, Submitted
Microscale Heat Transfer Lab – University of Virginia
Summary•DMM predicts hBD 850 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 trendsfor Cr/Si at room temperature
Microscale Heat Transfer Lab – University of Virginia
Today’s TalkPurpose: 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 > D) on hBD
Microscale Heat Transfer Lab – University of Virginia
Single phonon elastic scatteringElastic Scattering – hBD is a function of df/dT
j
jjBD
cutoffj
dcTfDT
h,1
0
1,1,11, ,4
1
Microscale Heat Transfer Lab – University of Virginia
Molecular Dynamics Simulations
Stevens, Zhigilei, and Norris, IJHMT, Accepted
0
0.4
0.8
1.2
1.6
2
0 0.1 0.2 0.3 0.4 0.5
Temperature [T *]
h* B
D/ h
* BD
( T*
=0.
25)
R=0.2
R=0.5
Linear(R=0.2)Linear(R=0.5)
Debye Temperature Ratios
R=0.5 trendline
R=0.2 trendline
Microscale Heat Transfer Lab – University of Virginia
Mismatched samples
Lyeo and Cahill, PRB, 2006Stoner and Maris, PRB, 1993
Microscale Heat Transfer Lab – University of Virginia
TTR Testing
Microscale Heat Transfer Lab – University of Virginia
hBD results
Ref 65. Stoner and Maris, PRB, 1993
Hopkins, Salaway, Stevens, and Norris, IJT, 2007
Microscale Heat Transfer Lab – University of Virginia
hBD resultsHopkins, Stevens, and Norris, JHT, 2007
Microscale Heat Transfer Lab – University of Virginia
Analysis• 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
10 100 100010-3
100
103
106
h BD [W
m-2K
-1]
Temperature [K]
j
jjBD
cj
dT
TfDch
,1
0
,11,1
),()(
4
1
DMM
JOINT FREQUENCY DMM
j
jjBD
cj
dT
TfDch
mod,
0
mod,1mod,
),()(
4
1
Microscale Heat Transfer Lab – University of Virginia
JFDMM
j
jjBD
cj
dT
TnDch
mod,
0
mod,1mod,
),()(
4
1
3mod,
2
2
mod,2 j
jc
D
cjmod,
3/1
22112
mod,mod, 6 NNc jc
j
2211mod, ccc j
212
1
12
1
1
MMNN
MNN
Microscale Heat Transfer Lab – University of Virginia
DMM vs. JFDMM
Microscale Heat Transfer Lab – University of Virginia
DMM vs. JFDMM
Microscale Heat Transfer Lab – University of Virginia
Summary
• 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 hBD around Debye Temperature
• Accounting for substrate phonon population in DMM improves prediction (JFDMM)
Microscale Heat Transfer Lab – University of Virginia
Conclusions & Acknowledgments
•Realistic interfaces – two phase regions, mixing, nonperfect junctions – multiple phonon scattering events that can decrease hBD
•Inelastic scattering can occur at elevated temperatures (T > D), increasing hBD
Purpose: Determine the effects that the properties of the interface have on thermal boundary conductance, 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
Microscale Heat Transfer Lab – University of Virginia
Resolving TBC with TTR
2df
BD
fi h
dC
1f
BD
i
f
k
dh
Resolving TBC with TTR Al/Al2O3 interfaces kf = 237 Wm-1K-1
hBD = 2.0 x 108 Wm-2K-1
0
0.5
1
1.5
0 25 50 75 100
Film thickness [nm]
Tim
e co
nsta
nt [n
s]
0
5
10
15
20
0 250 500 750 1000
if
Microscale Heat Transfer Lab – University of Virginia
Thermal ModelLumped capacitance
BD
f
f
BD
h
kd
k
dhBi
1.01.0
T
x
Bi<<1
Bi = 1
Bi>>1
film substrate Al/Al2O3 interfaces kf = 237 Wm-1K-1
hBD = 2.0 x 108 Wm-2K-1
d =75 nm< 120 nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 25 50 75 100
Film thickness [nm]
Tim
e c
on
sta
nt
[ns]
Microscale Heat Transfer Lab – University of Virginia
hBD trends vs. sample mismatch