Transition between ballistic and diffusive heat transport regimes in silicon materials

We study the extent of ballistic and diffusive thermal transport and the range of application of the Casimir and Fourier theories in semiconductor materials by using a theoretical model based on the Boltzmann transport equation. We show that combined effects of length scale, temperature, and boundary roughness are responsible for thermal transport transitions in silicon nanowires and thin films. We also introduce a more accurate principle for ballistic transport that considers the balance between internal and surface scattering. Phonon quantum confinement effects as well as the conditions for phonon wave interference in nanoscale heat transport are discussed.

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

[2]  Stephen B. Soffer,et al.  Statistical Model for the Size Effect in Electrical Conduction , 1967 .

[3]  A. Majumdar,et al.  Enhanced thermoelectric performance of rough silicon nanowires , 2008, Nature.

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

[5]  Yukihiro Tanaka,et al.  Phonon group velocity and thermal conduction in superlattices , 1999 .

[6]  M. Maldovan.  Thermal conductivity of semiconductor nanowires from micro to nano length scales , 2012 .

[7]  D. Cahill.  Thermal conductivity measurement from 30 to 750 K: the 3ω method , 1990 .

[8]  Paul Zschack,et al.  Ultralow Thermal Conductivity in Disordered, Layered WSe2 Crystals , 2007, Science.

[9]  H. Casimir.  Note on the conduction of heat in crystals , 1938 .

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

[11]  E. Pop,et al.  Impact of phonon-surface roughness scattering on thermal conductivity of thin si nanowires. , 2009, Physical review letters.

[12]  Xiang Lu.  Lattice thermal conductivity of Si nanowires: Effect of modified phonon density of states , 2008 .

[13]  G. Eesley,et al.  Transient thermoreflectance from thin metal films , 1986, Annual Meeting Optical Society of America.

[14]  D. Cahill,et al.  Ultra-Low Thermal Conductivity in W/Al2O3 Nanolaminates , 2004, Science.

[15]  Mehdi Asheghi,et al.  Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Layers , 2006 .

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

[17]  M. Maldovan.  Micro to nano scale thermal energy conduction in semiconductor thin films , 2011 .

[18]  Baowen Li,et al.  Thermal diode: rectification of heat flux. , 2004, Physical review letters.

[19]  N. Mingo.  Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations , 2003 .

[20]  Yiying Wu,et al.  Thermal conductivity of individual silicon nanowires , 2003 .

[21]  Mahan,et al.  Minimum thermal conductivity of superlattices , 2000, Physical review letters.

[22]  Kenneth E. Goodson,et al.  PHONON-BOUNDARY SCATTERING IN THIN SILICON LAYERS , 1997 .

[23]  M. Maldovan.  Thermal energy transport model for macro-to-nanograin polycrystalline semiconductors , 2011 .

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

[25]  William A. Goddard,et al.  Silicon nanowires as efficient thermoelectric materials , 2008, Nature.

[26]  A. Majumdar,et al.  Predicting the thermal conductivity of Si and Ge nanowires , 2003 .

[27]  Per Hyldgaard,et al.  Phonon superlattice transport , 1997 .

[28]  Alexander A. Balandin,et al.  Phonon heat conduction in a semiconductor nanowire , 2001 .

[29]  Kenneth E. Goodson,et al.  Heat Transfer Regimes in Microstructures , 1992 .

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

[31]  Mehdi Asheghi,et al.  Phonon–boundary scattering in ultrathin single-crystal silicon layers , 2004 .