1

Cross-plan Si/SiGe superlattice acoustic and thermal properties measurement by picosecond ultrasonics

Y. Ezzahri, S. Grauby, S. Dilhaire, J.M. Rampnouz, and W. ClaeysCentre de Physique Moléculaire Optique et Hertzienne (CPMOH), Université Bordeaux 1, 351

Cours de la Libération, 33405 Talence Cedex, France

JOURNAL OF APPLIED PHYSICSVol. 101

Pg. 013705 January 2007

Presented By:Thomas L. Steen

Department of Aerospace and Mechanical Engineering

2

• Paper Introduction

• Transient Thermoreflectance Technique

• Sample Description

• Experimental Setup

• Heat Transport Model

• Experimental Results• Acoustic Contributions• Thermal Contributions

• Summary

PRESENTATION OUTLINE

3

• 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

PAPER INTRODUCTION

4

• 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

TRANSIENT THERMOREFLECTANCE TECHNIQUE

J. L. Hostetler et al., Applied Optics, 38, p. 3614, (1999)

5

• 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

APPLICATIONS

R.J. Stevens et al., Journal of Heat Transfer, 127, p. 315, (2005)

J. L. Hostetler et al., Applied Optics, 38, p. 3614, (1999)

6

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

7

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

8

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

9

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

10

HEAT TRANSPORT MODEL

• Heat flow in the structure is governed by: T = temperature distributionC = specific heat per unit volume = normal component of thermal conductivity S(z,t) = heat source

• Initial and boundary conditions:R = reflection coefficientQ = pump pulse powerA = 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

11

LAPLACE DOMAIN

• Simplified in the Laplace domain:

• Boundary conditions:

sfsf pq ,2

, / fS /0

/1a

sfsfsf C ,,, )/(

*** Normal component of the thermal diffusivities

12

SOLUTION

sfsf pq ,2

, / fS /0

/1a

sfsfsf C ,,, )/(

*** Normal component of the thermal diffusivities

ffssff qBidqq )/(/

fKf RdBi /

• The temperature distribution inside the Al transducer:

13

REFLECTIVITY CHANGE

• The experimentally measured quantity is reflectivity• Develop a relationship between temperature variation and reflectivity

/1b

Four free parameters1. = heat source penetration depth 2. f

= thermal diffusivity of film3. 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)

14

SENSITIVITY ANALYSIS

• Sensitivity of R to the four free parameters

• Parameters are temporally uncorrelated• Sensitivity of reflectivity to s

is very weak

15

EXPERIMENTAL RESULTS

• Lock-in to the detector response at 574 kHz• Delay stage increases the time delay between pump and probe pulse

16

ACOUSTIC PROPERTIES

• Subtract the thermal background• 1 sample without cap layer• Measurement of Al transducer thickness

• Approximate the effective properties of the SL

• Measurement of the SL sound velocity

8.930.33 nm/ps

7.79 nm/ps

17

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

18

ACOUSTIC PROPERTIES

vsl (theory) = 7.79 nm/ps

19

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

20

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)

21

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

22

• Questions?