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
26
Embed
Ultrafast laser-based metrology for micron-scale ...
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
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