Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane.

The "textbook" phonon mean free path of heat carrying phonons in silicon at room temperature is ∼40  nm. However, a large contribution to the thermal conductivity comes from low-frequency phonons with much longer mean free paths. We present a simple experiment demonstrating that room-temperature thermal transport in Si significantly deviates from the diffusion model already at micron distances. Absorption of crossed laser pulses in a freestanding silicon membrane sets up a sinusoidal temperature profile that is monitored via diffraction of a probe laser beam. By changing the period of the thermal grating we vary the heat transport distance within the range ∼1-10  μm. At small distances, we observe a reduction in the effective thermal conductivity indicating a transition from the diffusive to the ballistic transport regime for the low-frequency part of the phonon spectrum.

[1]  Kenneth E. Goodson,et al.  Measurement of ballistic phonon conduction near hotspots in silicon , 2001 .

[2]  G. V. Chester,et al.  Solid-State Physics , 1962, Nature.

[3]  R. Pohl,et al.  Thermal boundary resistance , 1989 .

[4]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[5]  Cristina H. Amon,et al.  Cross-plane phonon transport in thin films , 2010 .

[6]  H. Dai,et al.  Photoexcited carrier diffusion near a Si(111) surface: Non-negligible consequence of carrier-carrier scattering , 1997 .

[7]  K. Nelson,et al.  Optical heterodyne detection of laser-induced gratings. , 1998, Optics letters.

[8]  Ronggui Yang,et al.  Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams. , 2010, Nature materials.

[9]  A. Majumdar.  Microscale Heat Conduction in Dielectric Thin Films , 1993 .

[10]  James J. Coleman,et al.  Ballistic-phonon heat conduction at the nanoscale as revealed by time-resolved x-ray diffraction and time-domain thermoreflectance , 2007 .

[11]  P. Leiderer,et al.  Optical temperature measurements on thin freestanding silicon membranes. , 2010, The Review of scientific instruments.

[12]  A. Majumdar,et al.  Nanoscale thermal transport , 2003, Journal of Applied Physics.

[13]  E. Pop.  Energy dissipation and transport in nanoscale devices , 2010, 1003.4058.

[14]  M. Dresselhaus,et al.  Thermal conductivity spectroscopy technique to measure phonon mean free paths. , 2011, Physical review letters.

[15]  Gang Chen,et al.  Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices , 1998 .

[16]  Gang Chen,et al.  Spectral Phonon Transport Properties of Silicon Based on Molecular Dynamics Simulations and Lattice Dynamics , 2008 .

[17]  E. H. Sondheimer,et al.  The mean free path of electrons in metals , 1952 .

[18]  J. Wolfe,et al.  Imaging Phonons: Contents , 1998 .

[19]  Gang Chen,et al.  Heat transport in silicon from first-principles calculations , 2011, 1107.5288.

[20]  Goldman,et al.  Ultrafast dynamics of laser-excited electron distributions in silicon. , 1993, Physical review letters.

[21]  N. Mingo,et al.  Intrinsic lattice thermal conductivity of semiconductors from first principles , 2007 .

[22]  Onset of nondiffusive phonon transport in transient thermal grating decay , 2011, 1108.3770.

[23]  David Broido,et al.  Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge , 2010 .

[24]  F. N. Frenkiel,et al.  Waves In Layered Media , 1960 .

[25]  Eichler,et al.  Laser-induced free-carrier and temperature gratings in silicon. , 1987, Physical review. B, Condensed matter.

[26]  Kenneth E. Goodson,et al.  Phonon scattering in silicon films with thickness of order 100 nm , 1999 .

[27]  Andrew G. Glen,et al.  APPL , 2001 .

[28]  David G. Cahill,et al.  Frequency dependence of the thermal conductivity of semiconductor alloys , 2007 .

[29]  Klaus Fuchs,et al.  The conductivity of thin metallic films according to the electron theory of metals , 1938, Mathematical Proceedings of the Cambridge Philosophical Society.

[30]  D. Pohl,et al.  Laser-Induced Dynamic Gratings , 1986 .

[31]  J. Rogers,et al.  Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications , 2000 .