Phonon lifetimes in silicon from 50 GHz to 15 THz - University of ...
Phonon lifetimes in silicon from 50 GHz to 15 THz - University of ...
Phonon lifetimes in silicon from 50 GHz to 15 THz - University of ...
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<strong>Phonon</strong> <strong>lifetimes</strong> <strong>in</strong> <strong>silicon</strong> <strong>from</strong> <strong>50</strong> <strong>GHz</strong> <strong>to</strong> <strong>15</strong> <strong>THz</strong><br />
David Cahill, Yux<strong>in</strong> Wang, Kwangu Kang,<br />
Fumiya Watanabe, Yee Kan Koh,<br />
and Jeffrey Letcher<br />
Department <strong>of</strong> Materials Science and Eng<strong>in</strong>eer<strong>in</strong>g<br />
and Materials Research Labora<strong>to</strong>ry,<br />
<strong>University</strong> <strong>of</strong> Ill<strong>in</strong>ois, Urbana, IL<br />
Brian Daly<br />
Vassar College, Poughkeepsie, NY
Experimental studies <strong>of</strong> <strong>silicon</strong> phonon<br />
<strong>lifetimes</strong> at room temperature<br />
• Attenuation <strong>of</strong> <strong>50</strong>-100 <strong>GHz</strong> longitud<strong>in</strong>al acoustic<br />
phonons measured by picosecond acoustics.<br />
–PRB 80, 174112 (2009).<br />
• Thermal acoustic phonons (1-10 10 <strong>THz</strong>) and reduction<br />
<strong>of</strong> thermal conductivity by mass disorder.<br />
–PRB 71, 235202 (2005); JAP 104, 024905 (2008).<br />
• Lifetimes <strong>of</strong> <strong>15</strong> <strong>THz</strong> optical phonons by timeresolved<br />
<strong>in</strong>coherent anti-S<strong>to</strong>kes Raman scatter<strong>in</strong>g.<br />
– APL 90, 252104 (2007).
Si phonon dispersion<br />
high-field carrier mobility, hot carrier pho<strong>to</strong>voltaics<br />
Thermal<br />
management,<br />
heat conduction<br />
acoustic imag<strong>in</strong>g, “phononics”
Time doma<strong>in</strong> thermoreflectance and<br />
picosecond acoustics<br />
• Improved optical design<br />
• Normalization by out-<strong>of</strong>-phase <strong>of</strong> signal elim<strong>in</strong>ates artifacts,<br />
<strong>in</strong>creases dynamic range and<br />
improves sensitivity<br />
• Exact analytical model for<br />
Gaussian beams and arbitrary<br />
layered geometries<br />
• One-laser/two-color approach<br />
<strong>to</strong>lerates diffuse scatter<strong>in</strong>g<br />
Clone built at Fraunh<strong>of</strong>er Institute for<br />
Physical Measurement, Jan. 7-8 2008
Time doma<strong>in</strong> thermoreflectance and<br />
picosecond acoustics<br />
• Optical constants and<br />
reflectivity depend on stra<strong>in</strong><br />
and temperature<br />
• Stra<strong>in</strong> echoes give acoustic<br />
properties p or film thickness<br />
• Thermoreflectance gives<br />
thermal properties
One and two round trips <strong>in</strong> <strong>50</strong> μm Si wafer<br />
Double-side polish th<strong>in</strong> Si wafer<br />
its)<br />
ΔR<br />
(Arbitr rary Un<br />
100K<br />
{ }<br />
{<br />
1<strong>50</strong>K<br />
200K<br />
× 2<br />
2<strong>50</strong>K × 2<br />
× 2 × 2<br />
Al film transducer<br />
{} 300K 12.22 12.3<br />
12.4<br />
24.6<br />
24.7<br />
24.8<br />
Delay Time (ns)
Broadband acoustic pulses<br />
• Fourier transforms <strong>of</strong> echoes <strong>from</strong> 10 nm (100 <strong>GHz</strong>)<br />
and 20 nm (<strong>50</strong> <strong>GHz</strong>) Al films<br />
Fourie er Transfo orm Amp plitude<br />
2.5<br />
1 Round Trip 1 Round Trip<br />
20 2.0<br />
'<strong>50</strong> <strong>GHz</strong>' '100 <strong>GHz</strong>'<br />
1.5<br />
05 0.5<br />
2 Round Trips<br />
'<strong>50</strong> <strong>GHz</strong>'<br />
1.0 2 Round Trips<br />
'100 <strong>GHz</strong>'<br />
0.0<br />
0.0 0.1 0.2 0.3<br />
Frequency (<strong>THz</strong>)
Analyze temperature dependence <strong>to</strong><br />
elim<strong>in</strong>ate surface effects<br />
Pea ak-Peak k<br />
Aco oustic Pulse Am mplitude<br />
e10<br />
1<br />
2 Round Trips<br />
1 Round Trip<br />
0 100 200 300<br />
Temperature (K)
f
TDTR enables measurements <strong>of</strong> epitaxial<br />
layers <strong>of</strong> high thermal conductivity<br />
• Time-doma<strong>in</strong> thermoreflectance (TDTR) data and model<br />
fit for iso<strong>to</strong>pically pure 28 Si<br />
– Two free parameters: thermal conductivity: Λ=164<br />
W/m-K; <strong>in</strong>terface conductance G=185 W/m 2 -K
Dilute SiGe alloys grown by gas-source<br />
molecular beam epitaxy<br />
Change <strong>in</strong> thermal resistance<br />
Δ W =Λ −Λ<br />
−1 −1<br />
28<br />
Ge concentration
Same truncated Debye-Callaway model<br />
predicts boundary scatter<strong>in</strong>g<br />
×2 reduction at ≈300 nm
Pump-probe Raman spectrometer
Time-resolved Raman spectra<br />
LO phonon<br />
t = 0.7 ps<br />
t = -10 ps
Time-resolved anti-S<strong>to</strong>kes <strong>in</strong>tensities<br />
‣ Integral <strong>of</strong> <strong>in</strong>tensity <strong>in</strong><br />
range 600-6<strong>50</strong> anti-<br />
S<strong>to</strong>kes wavenumbers<br />
gives electronic<br />
scatter<strong>in</strong>g by <strong>in</strong>terband<br />
hole excitations.<br />
‣ Integral (after<br />
background<br />
subtraction) <strong>of</strong> 490-5<strong>50</strong><br />
cm -1 gives <strong>in</strong>tensity <strong>of</strong><br />
LO phonon scatter<strong>in</strong>g<br />
‣ Pump power: 86 mW
Lifetime depends on pho<strong>to</strong>excited<br />
carrier density<br />
Lifetime <strong>from</strong> Raman l<strong>in</strong>ewidth<br />
• At low excitation,<br />
lifetime approaches<br />
prediction <strong>from</strong><br />
Raman l<strong>in</strong>ewidth:<br />
pure-dephas<strong>in</strong>g is not<br />
important.<br />
• Lifetime <strong>of</strong> zone<br />
center phonons<br />
decreases at higher<br />
excitation. Spectral<br />
diffusion? Enhanced<br />
coupl<strong>in</strong>g <strong>to</strong> acoustic<br />
modes?
Summary<br />
• Lifetime <strong>of</strong> 100 <strong>GHz</strong> longitud<strong>in</strong>al phonons is ~5 nsec; fit<br />
<strong>to</strong> Akhieser mechansims gives thermal phonon lifetime<br />
2<br />
2<br />
<strong>of</strong> ~20 ps assum<strong>in</strong>g γ − γ = 1<br />
• Model fits <strong>to</strong> thermal conductivity <strong>of</strong> iso<strong>to</strong>pically pure Si<br />
and ddilute SiGe alloys is consistent t with dom<strong>in</strong>ant<br />
mean-free-path for heat carry<strong>in</strong>g phonons <strong>of</strong> 300 nm.<br />
Lifetime ~30 ps.<br />
• Lifetime <strong>of</strong> zone-center optical phonon is 2 ps but<br />
depends on carrier (hole) density.