Measurement of thermal conductivity Part A: P Part B: t B Time - - PowerPoint PPT Presentation

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Measurement of thermal conductivity Part A: P Part B: t B Time - - PowerPoint PPT Presentation

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Measurement of thermal conductivity Part A: P Part B: t B Time domain thermoreflectance = effusivity C Modified Angstrom method takes into account thermal conductance from sidewalls to ambient Modern application to suspended

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Measurement of thermal conductivity

Part A: P t B Part B:

  • Time domain thermoreflectance
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C Λ =

effusivity

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Modified Angstrom method takes into account thermal conductance from sidewalls to ambient Modern application to suspended polycrystalline Si microcantilevers (10 micron width) microcantilevers (10 micron width)

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  • At high temperatures,

h i i l i h

2

anharmonicity also increases the heat capacity – thermal expansion causes the f

2 P V

C C VT α κ − =

vibrational modes to soften, increasing the vibrational entropy per atom

V

C V α κγ =

α = volume coefficient of thermal expansion

3 1

V B P

C Nk C T =

γ = Grüneisen constant κ = compressibility

1 3

P B

T Nk αγ − =

1 dV V dT α =

D D

d V dV γ Θ = Θ

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Can get around this with a Can get around this with a multilayer where at least

  • ne layer is known
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Typical calibration of Au film resistance vs. T

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( ) ( ) P T r K qr lπ Δ = Λ

Solution for an infinite half-space

lπΛ

K0 is the zeroth order modified Bessel function Think of this as the circular thermal wave Take the Fourier transform of this frequency domain solution

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For a low thermal conductivity thin film For a low thermal conductivity thin film

  • n a high thermal conductivity substrate

(Factor of 2 because current is at frequency ω) (Factor of 2 because current is at frequency ω)

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Thermoreflectance Methods

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Measurement of Thermal Conductivity Part B: Time-domain thermoreflectance

David G. Cahill, Materials Research Lab and Department of Materials Science, U. of Illinois

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Time-domain thermoreflectance

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Time-domain thermoreflectance

Clone built at Fraunhofer Institute for Physical Measurement, Jan. 7-8 2008

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psec acoustics and time-domain thermoreflectance

  • Optical constants and

reflectivity depend on strain and temperature

  • Strain echoes give

acoustic properties or acoustic properties or film thickness

  • Thermoreflectance gives

th l ti thermal properties

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Schmidt et al., RSI 2008

  • Heat supplied by

modulated pump p p beam (fundamental Fourier component at frequency f) at frequency f)

  • Evolution of surface
  • Evolution of surface

temperature

time

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Schmidt et al., RSI 2008

  • Instantaneous

temperatures measured by time-delayed probe

  • Probe signal as

measured by rf lock-in measured by rf lock in amplifier

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Analytical solution to 3D heat flow in an infinite half-space, Cahill, RSI (2004)

  • spherical thermal wave
  • Hankel transform of

surface temperature

  • Multiply by transform
  • f Gaussian heat

source and take source and take inverse transform

  • Gaussian-weighted
  • Gaussian-weighted

surface temperature

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Iterative solution for layered geometries

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Signal analysis for the rf lock-in

  • In-phase and out-of-phase signals by series of sum and

difference over sidebands

  • ut-of-phase signal is dominated by the m= 0 term
  • ut of phase signal is dominated by the m= 0 term

(frequency response at modulation frequency f)

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Windows software

author: Catalin Chiritescu author: Catalin Chiritescu, users.mrl.uiuc.edu/ cahill/ tcdata/ tdtr_m.zip

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Thermoreflectance data for isotopically pure Si p

  • Two free fitting parameters

– thermal conductivity, 165 W/ m-K – Al/ Si interface conductance, 185 MW/ m 2-K

Phoenix, Arizona 11

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Time-domain Thermoreflectance (TDTR) data for TiN/ SiO2/ Si

SiO2

TiN Si

  • reflectivity of a metal

depends on temperature temperature

  • one free parameter:

the “effective” thermal conductivity

  • f the thermally

grown SiO2 layer

2

(interfaces not modeled separately)

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TDTR: early validation experiments

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Nothing really new...just faster and smaller

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Thermal conductivity mapping

  • At t= 100 ps
  • At t= 100 ps,

– in-phase signal is determined by the heat capacity of the Al film capacity of the Al film – out-of-phase signal is mostly determined by the effusivity (ΛC) 1/ 2 of the substrate

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Thermal barrier coatings

  • cross section of e-beam

ZrO2: Y coating on (Ni,Pt)Al bond coat on Ni based bond-coat on Ni-based super-alloy (Rene N5)

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ZrO2: Y thermal barrier

500 th l l

  • 500 thermal cycles

between room temperature and engine p g

  • perating temperature
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ZrO2: Y thermal barrier, depth profile

  • penetration depth of

thermal waves is 100 nm

  • angle polish and measure

along a line to create a g depth profile

  • dull but important result:

thermal conductivity is isotropic and homogeneous