Cross-plan Si/SiGe superlattice acoustic and thermal
properties measurement by picosecond ultrasonics
Y. Ezzahri, S. Grauby, S. Dilhaire, J.M. Rampnouz, and W. Claeys
Centre de Physique Moléculaire Optique et Hertzienne (CPMOH), Université Bordeaux 1, 351
Cours de la Libération, 33405 Talence Cedex, France
JOURNAL OF APPLIED PHYSICS
Vol. 101
Pg. 013705
January 2007
Presented By:
Thomas L. Steen
Department of Aerospace and Mechanical Engineering
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PRESENTATION OUTLINE
• Paper Introduction
• Transient Thermoreflectance Technique
• Sample Description
• Experimental Setup
• Heat Transport Model
• Experimental Results
• Acoustic Contributions
• Thermal Contributions
• Summary
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PAPER INTRODUCTION
• Si/SiGe superlattice (SL) grown on silicon substrate
• Nondestructive evaluation of thermal and acoustic
properties
• Thermal boundary resistance between Al/SL
• SL thermal conductivity
• Longitudinal sound velocity inside SL
• Pump-probe thermoreflectance technique (PPTT)
• Heat the surface with an intense “pump” beam
• Monitor reflectivity variations of the surface with a
weaker “probe” beam
• Extract thermal conductivity and interface thermal
resistance
• Implement a heat transport model
• Compare experimental cooling curves with theoretical
model
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TRANSIENT THERMOREFLECTANCE TECHNIQUE
• Measurement involving two laser pulses of a few picoseconds
• Pump pulse produces ultrafast heating
• Thermally induced change in the refractive index of
surface
• Measured with a weaker probe pulse
• Variably delayed with respect to the pump beam
J. L. Hostetler et al., Applied Optics, 38, p. 3614, (1999)
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APPLICATIONS
• Technique has been applied for measuring:
• Thermal diffusion in thin films
• Sound velocities
• Electron-phonon coupling factors of metal films
• Thermal boundary resistance
• Thermal property imaging
J. L. Hostetler et al., Applied Optics, 38, p. 3614, (1999)
R.J. Stevens et al., Journal of Heat Transfer, 127, p. 315, (2005)
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SAMPLE DESCRIPTION
• 1 µm thick Si/Si0.7Ge0.3 superlattice (SL)
• Grown on 500 µm silicon substrate
• Coated with an Al “transducer” film
• Role of the metal film
• Convert light energy into heat and the creation
of acoustic waves
• Thickness = 86 to 474 nm
• 2 µm SiGe/SiGeC buffer layer
• Reduce mechanical stress
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EXPERIMENTAL SETUP
• Pump/Probe intensity ratio of 10:1
• Probe monitors the reflectivity variation of the metal film surface
• Pump beam passes through an acousto-optic modulator (AOM)
• Creates a pulse train modulated at 574 kHz
• Lock-in to the detector response at 574 kHz
• Pump beam ~ 20 µm
• Delay stage increases the time delay between pump and probe pulse
• Probe beam ~ 6 µm
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EXTRACTING THERMAL PROPERTIES
• Compare experimental cooling curves to a theoretical
model to extract:
• Thermal boundary resistance
• Thermal conductivity of SL
• Sound velocity in SL
• Pump light absorbed at Al film surface
• Excite electrons to higher energy states
• Constitutes heat source
• Diffuses away form the Al surface
• Heat source penetration depth = 
•  >> 
• Confined in the Al film
• Within several picoseconds, hot electrons transfer
their energy to the SL
• Phonon emission
•  = optical penetration depth
•  = 7nm at  = 780nm for Al
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HEAT TRANSPORT MODEL
• Experiment time scale ~ 1ns
• Transducer thickness >> 
• Heat diffusion within metal cannot be neglected
• Model heat propagation using the Fourier classical heat diffusion equation
• Assumptions
• Penetration of heat source inside transducer is being taken into account
• SL layer behaves like semi-infinite medium
• No effect from buffer layer or Si substrate
• 1D thermal problem
• Large pump diameter (~20µm)
• Heat flux at the free surface of the Al not taken into account
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HEAT TRANSPORT MODEL
• Heat flow in the structure is governed by:
T = temperature distribution
C = specific heat per unit volume
 = normal component of thermal conductivity
S(z,t) = heat source
• Initial and boundary conditions:
R = reflection coefficient
Q = pump pulse power
A = surface area illuminated by pump
(t) = Dirac delta function
• Continuity of heat flux at Al/subjacent layer interface:
• Thermal behavior of this interface:
RK = Thermal boundary resistance
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LAPLACE DOMAIN
• Simplified in the Laplace domain:
q 2f ,s  p /  f ,s
  S0 /  f
a  1/ 
 f ,s   f,s /( C ) f ,s
• Boundary conditions:
*** Normal component of the thermal diffusivities
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SOLUTION
• The temperature distribution inside the Al transducer:
   f q f /  s qs  (d f / Bi )q f
Bi  d f / RK  f
q 2f ,s  p /  f ,s
  S0 /  f
a  1/ 
 f ,s   f,s /( C ) f ,s
*** Normal component of the thermal diffusivities
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REFLECTIVITY CHANGE
• The experimentally measured quantity is reflectivity
• Develop a relationship between temperature variation and reflectivity
b  1/ 
Four free parameters
1.  = heat source penetration depth
2. f = thermal diffusivity of film
3. s = thermal diffusivity of the
subjacent layer
4. RK = interface thermal resistance
***Numerical algorithm applied to calculate the
inverse Laplace transform and obtain R(t)
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SENSITIVITY ANALYSIS
• Sensitivity of R to the four free parameters
• Parameters are temporally uncorrelated
• Sensitivity of reflectivity to s is very weak
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EXPERIMENTAL RESULTS
• Lock-in to the detector response at 574 kHz
• Delay stage increases the time delay
between pump and probe pulse
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ACOUSTIC PROPERTIES
• Subtract the thermal background
• 1 sample without cap layer
• Measurement of Al transducer thickness
• Approximate the effective properties of the SL
7.79 nm/ps
• Measurement of the SL sound velocity
8.930.33 nm/ps
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ACOUSTIC PROPERTIES
• 3 samples with cap layer
• 86nm and 186nm films
• Measure Al thickness
• 2 echoes from Al/cap interface
• Cap thickness (1st and 3rd echoes)
• SL sound velocity (3rd and 4th echoes)
• 474nm film
• Measure Al thickness
• 2nd echo from Al/cap interface
disappears
• Cap thickness (1st and 2nd echoes)
• SL sound velocity (2nd and 3rd echoes)
• 5 bursts
• buried layers in the buffer layer
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ACOUSTIC PROPERTIES
vsl (theory) = 7.79 nm/ps
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THERMAL PROPERTIES
• Optimize the free parameters: , f, s, and RK
• Fast thermal decay depends mainly on  and f
• Second part controlled by RK
• Sensitivity of reflectivity to s is very weak
• Thick Al transducer (474nm) – heat does not cross transducer
during short time scale of experiment
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THERMAL PROPERTIES
• 105nm transducer – used a previously extracted value for s identified
when SL covered by very thin (12nm) Al film
• Cap layer hides the SL (86 nm and 186 nm transducer)
• Results show that  >> 
Ezzahri et al., Appl. Phys. Lett. 87, 103506 (2005)
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SUMMARY
• Characterization of Si/SiGe superlattice using pump-probe
thermoreflectance technique
• Analyze thermal and acoustic contributions
• Unsuccessful in extracting thermal conductivity of SL
• To increase sensitivity to SL thermal properties:
• Long pump-probe delay
• Thin metal transducer
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• Questions?
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