Transcript Thermo-elastic properties characterization by photothermal

Thermo-elastic properties characterization by
photothermal microscopy
J.Jumel,F.Taillade and F.Lepoutre
Eur. 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
Temperature distribution of the sample
• Description of the Thermal Problem
Three dimensional Heat Equation
1
1 T (r , t )
 T (r , t )  g (r , t ) 
k
 t
2
R{, }, t  0
T(r,t) - Temperature distribution (K)
g(r,t) -
P (r  r0 )e jt
(W/m3)
K - thermal conductivity of the sample (W/m-K)
 - thermal diffusivity of the sample (m2/sec)
wseTemperature Distribution of the Sample
Solution by Green's function method :
r1
r1

j ( t  )
P


 T (r1 , t ) 
e e
4 Kr1
r1  r  r0


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
Periodic fluctations of I(t) about I0R0
 1 R

 (r1 , t )  R0 I 0 
 T (r1 , t ) 
 R0 T

• Temperature modulation leads to modulation of the reflection coefficient R
R 1 dR

T
R0 R0 dT
• Total reflected Light
Where
1 dR - coefficient of thermal reflectance
R0 dT
 R 
I (t )  I 0 R0 1 

R
0 

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
dr


d
f
  18mm2 / sec
Experimental Results:
Tantalum Sample
Thermal diffusivity23.8 mm2/sec
• Linear Phase Variation
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
• 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

4

 h   d 
h - surface altitude variation
 - splitting angle of wollaston prism
 - wavelength of the laser
d - distance that can be adjusted by piezotranslation stage
1. Beam Splitter
2. Quarter Wave plate
3. Wollaston Prism
4. Microscope objective
5. Sample
Interference Signal
The DC Signal measured at the photodetector is
I
1
R  R2
f 0 I 0 R1  R2  2 R1 R2 cos( )  (1  f 0 ) I 0 1
4
2


R1, R2 - reflection coefficient of the two beams
F0 - ratio of the common surface between the two beams to section surface
Of a single beam on the photodiode.
• The periodic elevation Uz of the sample modulates the
phase lag about 
• Produces a harmonic term Usin where
U 
R1R2
4
f0 I0
Uz
2

• 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
I  T (1  A cos  )  U sin   f ( B cos   1)
F- photodeflection signal
T - photothermal signal
A 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
U
I ( / 2)  I ( / 2)
2
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.
For a small pump radius rg
Minimum phase:
r

 4.55
Cut - Off Position
r

 5.47
Phase minimum and cut off as function of thermal diffusion length is plotted
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 beam
Of 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 variationquasi sinusoidal with 3 periods
• Four periods (cubic symmetry) for [100]
• Two periods (orthotropic symmetry) for [110]
Modulation at 500 KHz
Offset Pump- Probe : 10 microns
Experimental Results - Phase Plots -100 KHz
[110]
[1 0 0]
[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