Thermo-elastic properties characterization by photothermal microscopy J.Jumel,F.Taillade and F.Lepoutre Eur. Phys. J. AP 23,217-225 Journal Club Presentation.

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