Theoretical phonon thermal conductivity of Si/Ge superlattice nanowires

An incoherent particle model has been developed to calculate the phonon thermal conductivity of superlattice nanowires. This is an extension of the photon net-radiation method and Schuster–Schwarzschild approximation to dispersive acoustic phonons in a gray medium. By comparing the roughness and geometric variations of typical nanowires to the characteristic phonon wavelength (∼1 nm at 300 K), diffuse scattering and incoherent three-dimensional dispersion are justified. An isotropic sine-type (Born–von Karman) dispersion is used, which requires only the sound velocity, atomic number density, and bulk conductivity to fully describe a material. A simple picture is also given in terms of Matthiessen’s rule and three effective mean free paths. Agreement with available experimental data is poor at the smallest diameters, but good above 30 nm diameter. Compared to a conventional superlattice, calculations show that the additional sidewall scattering in a superlattice nanowire can reduce the thermal conductivity...

[1]  Paul G. Klemens,et al.  Thermal Resistance due to Point Defects at High Temperatures , 1960 .

[2]  M. G. Holland.  Analysis of Lattice Thermal Conductivity , 1963 .

[3]  D. Broido,et al.  Lattice thermal conductivity of wires , 1999 .

[4]  John Ziman,et al.  Thermal conduction in artificial sapphire crystals at low temperatures I. Nearly perfect crystals , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[5]  Lars Samuelson,et al.  One-dimensional steeplechase for electrons realized , 2002 .

[6]  Peidong Yang,et al.  Block-by-Block Growth of Single-Crystalline Si/SiGe Superlattice Nanowires , 2002 .

[7]  B. Abeles.  Lattice Thermal Conductivity of Disordered Semiconductor Alloys at High Temperatures , 1963 .

[8]  Mildred S. Dresselhaus,et al.  Effect of quantum-well structures on the thermoelectric figure of merit. , 1993, Physical Review B (Condensed Matter).

[9]  Michael L. Roukes,et al.  Phonon scattering mechanisms in suspended nanostructures from 4 to 40 K , 2002 .

[10]  J. Chu,et al.  Size effect on the thermal conductivity of nanowires , 2002 .

[11]  R. Venkatasubramanian,et al.  Thin-film thermoelectric devices with high room-temperature figures of merit , 2001, Nature.

[12]  H. Bilz,et al.  Phonon Dispersion Relations in Insulators , 1979 .

[13]  M. Dresselhaus,et al.  Thermoelectric figure of merit of a one-dimensional conductor. , 1993, Physical review. B, Condensed matter.

[14]  Sebastian Volz,et al.  Molecular dynamics simulation of thermal conductivity of silicon nanowires , 1999 .

[15]  Charles M. Lieber,et al.  Growth of nanowire superlattice structures for nanoscale photonics and electronics , 2002, Nature.

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

[17]  H. Maris,et al.  Kapitza conductance and heat flow between solids at temperatures from 50 to 300 K. , 1993, Physical review. B, Condensed matter.

[18]  N. Snyder.  HEAT TRANSPORT THROUGH HELIUM II: KAPITZA CONDUCTANCE. , 1970 .

[19]  G. A. Slack,et al.  Thermal Conductivity of Silicon and Germanium from 3°K to the Melting Point , 1964 .

[20]  Fischer,et al.  Phonon radiative heat transfer and surface scattering. , 1988, Physical review. B, Condensed matter.

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

[22]  Charles M. Lieber,et al.  Epitaxial core–shell and core–multishell nanowire heterostructures , 2002, Nature.

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

[24]  H. Goldsmid,et al.  The effect of boundary scattering on the high-temperature thermal conductivity of silicon , 1973 .

[25]  M. Modest.  Radiative heat transfer , 1993 .

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

[27]  Michael L. Roukes,et al.  Direct thermal conductance measurements on suspended monocrystalline nanostructures , 1997 .

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

[29]  D. Rowe.  CRC Handbook of Thermoelectrics , 1995 .

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

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

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

[33]  Gang Chen.  Phonon wave heat conduction in thin films and superlattices , 1999 .

[34]  Yu-Ming Lin,et al.  Thermoelectric properties of superlattice nanowires , 2003 .

[35]  Gang Chen,et al.  Partially coherent phonon heat conduction in superlattices , 2003 .

[36]  J. Ziman,et al.  The thermal conductivity of germanium and silicon between 2 an d 300° K , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[37]  J. M. Worlock,et al.  Measurement of the quantum of thermal conductance , 2000, Nature.

[38]  J. Ziman,et al.  In: Electrons and Phonons , 1961 .