Thermo-elastic properties characterization by photothermal microscopy J.Jumel,F.Taillade and...
-
date post
22-Dec-2015 -
Category
Documents
-
view
215 -
download
0
Transcript of Thermo-elastic properties characterization by photothermal microscopy J.Jumel,F.Taillade and...
Thermo-elastic properties characterization by photothermal microscopy
J.Jumel,F.Taillade and F.LepoutreEur. Phys. J. AP 23,217-225
Journal Club Presentation
5/15/06
Presenter: AshwinKumar
Outline• Motivation
• Thermal Characterization of bulk isotropic media by photothermal microscopy
* Temperature distribution of the surface
* Characterization of thermal wave propogation
* Photoreflectance Technique • Experimental Setup
* Photoreflectance Configuration
* Interferometer Configuration(Normarski)
• Microscopic Thermoelastic characterization
* Analysis of the interferometric signal
* Isotropic media characterization
* Anisotropic media chracterization
• Summary
Motivation
• A better understanding of the microscopic physical mechanisms is pivotal.
• Sample response - photothermal experiment - dependant on thermoelastic parameters
• Photoreflectance Technique allows accurate characterization of thin films , interfaces and composites
• Determination of thermo-elastic parameters such as thermal diffusivity ,elastic anistropy and crystalline orientation - surface displacements by interferometry
Thermal characterization of bulk isotropic media by photothermal microscopy
1 Electromagnetic flux
2 Sample
3 Periodic Temperature rise
4 Periodic Surface Displacement
5 Refractive index Variation
6 Infra Red emissions
7 Acoustic emissions
• Description of the Thermal Problem
Three dimensional Heat Equation
Temperature distribution of the sample
2 1 1 ( , )( , ) ( , )
T r tT r t g r t
k t
R{ , }, 0t
T(r,t) - Temperature distribution (K)
g(r,t) - (W/m3)
K - thermal conductivity of the sample (W/m-K) - thermal diffusivity of the sample (m2/sec)
0( ) j tP r r e
wseTemperature Distribution of the Sample
Solution by Green's function method :
1 1( )
11
1 0
( , )4
r rj tP
T r t e eKr
r r r
f
K
C
- thermal diffusion length
The phase lag varies linearly with r1
Thermal diffusivity can be obtained from the thermal wave number
Thermal waves are heavily damped
Higher the modulation frequency , faster the amplitude decreases
Typically f ~ 100 KHz , ~ 1 cm2/sec , confinement volume is about a few cubic microns - determines the thermal resolution of the method
Photoreflectance Technique
• Temperature modulation leads to modulation of the reflection coefficient R
0 0
1R dRT
R R dT
Where
0
1 dR
R dT - coefficient of thermal reflectance
• Total reflected Light
0 00
( ) 1R
I t I RR
Periodic fluctations of I(t) about I0R0
1 0 0 10
1( , ) ( , )
Rr t R I T r t
R T
Experimental Setup
• Control of dichoric mirror controls the pump-probe position r1
• Pump beam is scanned at
sample surface
• Interferometrer Configuration obtained by the addition of parts 18 and 19
Experimental Results:• Sample - Nickel - 200 KHz
• Circular aspect of the isotherms confirms the isotropic behavior
• distance measurement between consecutive isophase lines gives the thermal diffusion length
Thermal diffusivity
218 / sec
dr
d f
mm
Experimental Results: • Linear Phase Variation
Tantalum Sample
Thermal diffusivity-
23.8 mm2/sec
Experimental Setup
• Control of dichoric mirror controls the pump-probe position r1
• Pump beam is scanned at
sample surface
• Interferometrer Configuration obtained by the addition of parts 18 and 19
Nomarski Interferometer
1. Beam Splitter2. Quarter Wave plate3. Wollaston Prism4. Microscope objective5. Sample
• Wollaston Prism - Splits probe beam - Two orthogonal polarized beams
• Two spots are focused onto the sample seperated by a few microns
• The height difference between the two spots introduces a optical path length difference
• Wollaston prism produces a static phase lag given by
4h d
h - surface altitude variation - splitting angle of wollaston prism - wavelength of the laserd - distance that can be adjusted by piezo-translation stage
Interference Signal
The DC Signal measured at the photodetector is
1 20 0 1 2 1 2 0 0
12 cos( ) (1 )
4 2
R RI f I R R R R f I
R1, R2 - reflection coefficient of the two beamsF0 - ratio of the common surface between the two beams to section surfaceOf a single beam on the photodiode.
• The periodic elevation Uz of the sample modulates the phase lag about
• Produces a harmonic term Usin where
1 20 0
4
2 z
R RU f I U
• Photothermal effects cause modulation of reflection coefficient R1• Non -uniform surface displacement and a possible thermal lens effect causes the beam to defocus and deviate periodically• Makes f0 to oscillate about it's mean value giving rise to a photodeflection signal
Total Signal at the Photodetector(1 cos ) sin ( cos 1)I T A U f B
F- photodeflection signalT - photothermal signalA and B are experimental parameters related to interference fringe amplitude and contrast
• At = 0 or , a pure interferometric term would have the same value, but spurious effects are seen
• To extract interferometric signal , we take measurements at = -/2 and /2
• U is obtained by ( / 2) ( / 2)
2
I IU
Reconstruction of the Signal
Sample : AlPdMn quasi crystal modulated at 100 KHz
Isotropic Media Characterization
• The position where the phase has a minimum is found by multiparameter least square regression fitting.
Phase minimum and cut off as function of thermal diffusion length is plotted
For a small pump radius rg
Minimum phase:
4.55r
Cut - Off Position
5.47r
Isotropic Media Characterization
Thermal Diffusivity obtained from (AlPdMn sample , 100 KHz) is 0.54 +/- 0.1 mm2/sec
Anisotropic Media Characterization
Simulation of out-of plane response of Ni [1 1 1] at 500KHz and using a Gaussian beamOf radius 1 micron.
•Anisotropy not quite evident in the attenuation plot•The phase plot shows distinct features of anisotropy
Experimental Results
• Most Significant contrast is observed for [111] with phase variation- quasi sinusoidal with 3 periods
• Four periods (cubic symmetry) for [100]
• Two periods (orthotropic symmetry) for [110]
Modulation at 500 KHzOffset Pump- Probe : 10 microns
Experimental Results - Phase Plots -100 KHz
[1 0 0] [110]
[111]
Summary
• Simultaneous Thermal and thermoelastic characterizations at a micrometer scale can be performed
• Experimental Setup allows photoreflectance and interferometric configurations
• Extraction of thermal diffusivity from photodisplacement and photoreflectance measurements were shown.
• Phase measurements have shown to be very sensitive to anisotropy in the media