STUDY OF PHONON HEAT TRANSFER IN METALLIC SOLIDS FROM MOLECULAR DYNAMICS SIMULATIONS (original) (raw)
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Journal of Applied Physics, 2016
The effect of phonon-electron (p-e) scattering on lattice thermal conductivity is investigated for Cu, Ag, Au, Al, Pt, and Ni. We evaluate both phonon-phonon (p-p) and p-e scattering rates from first principles and calculate the lattice thermal conductivity (j L). It is found that p-e scattering plays an important role in determining the j L of Pt and Ni at room temperature, while it has negligible effect on the j L of Cu, Ag, Au, and Al. Specifically, the room temperature j L s of Cu, Ag, Au, and Al predicted from density-functional theory calculations with the local density approximation are 16.9, 5.2, 2.6, and 5.8 W/m K, respectively, when only p-p scattering is considered, while it is almost unchanged when p-e scattering is also taken into account. However, the j L of Pt and Ni is reduced from 7.1 and 33.2 W/m K to 5.8 and 23.2 W/m K by p-e scattering. Even though Al has quite high electron-phonon coupling constant, a quantity that characterizes the rate of heat transfer from hot electrons to cold phonons in the two-temperature model, p-e scattering is not effective in reducing j L owing to the relatively low p-e scattering rates in Al. The difference in the strength of p-e scattering in different metals can be qualitatively understood by checking the amount of electron density of states that is overlapped with the Fermi window. Moreover, j L is found to be comparable to the electronic thermal conductivity in Ni. Published by AIP Publishing.
Analysis of Phonon Heat Conductivity of Semiconductors
The various inadequacies of Callaway's phenomenological model of lattice thermal conductivity has been critically analyzed and the model is repaired in a modified form in which the systematic replacement of life time by line widths amicably resolves the various issues. The involvement of various scattering events in the heat transport, e.g., boundary scattering, impurity scattering, anharmonic phonon scattering, resonance scattering and interference scattering has been addressed in the new framework with the help of quantum dynamical many body theory. The technological importance of Ge is well known and hence it becomes significantto investigate the thermal behavior of it in details as its electrical properties are temperature dependent. Further, the CdTe also shows its vital importance in the fabrication of infrared optical windows and photo voltaic solar cells. The phonon heat conductivity of Ge and CdTe in the temperature range 3.3-298 K and 1.780-239.260 K based on the modified Callaway model have been analyzed and excellent agreements between theory and experiments are reported. The present formulation is found to be well justified and can be successfully applied for the calculations of thermal conductivity of several other crystalline solids.
Physical Review B, 2010
The Boltzmann transport equation is used to calculate thermal and electrical conductivity of metal nanostructures with characteristic dimensions in the 25-500 nm range, near to and above the Debye temperature. Thermal conductivity contributions from phonons and electrons are considered. The intrinsic effects of electron-phonon, phonon-phonon, and phonon-electron scattering, and grain boundary and surface interactions are addressed. Excellent agreement is found between model results and available data reporting direct measurements of thermal conductivity of nanowires, ribbons, and thin films in Al, Pt, and Cu, respectively. The Wiedemann-Franz ͑W-F͒ law and Lorenz factor are examined with decreasing size; their applicability is found to degrade in nanowires due mainly to increased relative phonon contribution. The effect of differences in the electron mean-free path for thermal gradient versus electrical field is also examined. A modified version of W-F is presented, corrected for these two factors and valid from macroscale to nanoscale provided characteristic sizes exceed the phonon mean-free path.
Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation
International Journal of Heat and Mass Transfer, 2009
In this study, the influence of phonon dispersion approximation on the prediction of in-plane and out-ofplane thermal conductivity of thin films and nanowires is shown. Results obtained using the famous Holland dispersion approximation and the Brillouin zone boundary condition (BZBC) dispersion curves are compared. For (in-plane and out-of-plane) thermal conductivity predictions based on BZBC dispersion curves, new relaxation time parameters fitted from experimental data of bulk silicon thermal conductivity are reported. The in-plane thermal conductivity of nanostructures (films of thicknesses 20 nm, 100 nm, and 420 nm and nanowires of widths 22 nm, 37 nm, and 100 nm) in the temperature range 20-1000 K is calculated from the modified bulk thermal conductivity model by scaling the bulk phonon mean free path (MFP) by the Fuch-Sondheimer factor of boundary scattering developed for nanostructures with rectangular cross-section. The pseudo out-of-plane thermal conductivity of films of thicknesses 20 nm, 100 nm, and 420 nm and in the temperature range 150-1000 K is calculated from the solution of the Boltzmann transport equation (BTE) for phonons by using the Discrete ordinate method (DOM), and the Monte Carlo (MC) simulation. In order to confirm the current results, the calculated in-plane thermal conductivity of silicon thin films and silicon nanowires are compared with existing experimental data. Moreover, due to lack of experimental and theoretical data of out-of-plane thermal conductivity of thin films, comparison of the DOM and MC simulation is performed. The current work shows that a drastic simplification of dispersion curves can lead to wrong prediction of both in-plane and out-of-plane thermal conductivities of nanostructures, especially for ultra thin nanostructures and/or at high temperatures. Comparison with experimental data of in-plane thermal conductivity of silicon thin films and silicon nanowires proves that more refined dispersion approximation such as the BZBC is well adequate for phonon transport calculations when confinement has negligible effect. Moreover, the comparison between the thermal conductivity in the out-of-plane direction and that in the inplane direction enables one to quantify the anisotropy of thermal conductivity of the film.
Physical Review B
The Boltzmann transport equation is used to calculate thermal and electrical conductivity of metal nanostructures with characteristic dimensions in the 25-500 nm range, near to and above the Debye temperature. Thermal conductivity contributions from phonons and electrons are considered. The intrinsic effects of electron-phonon, phonon-phonon, and phonon-electron scattering, and grain boundary and surface interactions are addressed. Excellent agreement is found between model results and available data reporting direct measurements of thermal conductivity of nanowires, ribbons, and thin films in Al, Pt, and Cu, respectively. The Wiedemann-Franz ͑W-F͒ law and Lorenz factor are examined with decreasing size; their applicability is found to degrade in nanowires due mainly to increased relative phonon contribution. The effect of differences in the electron mean-free path for thermal gradient versus electrical field is also examined. A modified version of W-F is presented, corrected for these two factors and valid from macroscale to nanoscale provided characteristic sizes exceed the phonon mean-free path.
Thermal conduction at the nanoscale in some metals by MD
Microelectronics Journal, 2003
Miniaturization of electronic devices leads to nanoscale structures in the near future. As the system size decreases the heat dissipation density increases rapidly and the heat conduction becomes an important problem. Moreover, in very small systems the conduction is a size dependent phenomenon-conductivity decreases as the size decreases. We study the thermal conduction by phonons and its size dependency in seven metals, most of which are important in electronics. We use the molecular dynamic method with embedded atom potentials.
Electron-phonon interaction and lattice thermal conductivity
Physical Review B, 1978
Phonons in a metal have a finite lifetime due to the emission of electron-hole pairs. This process leads to an electron-phonon contribution W, '" to the thermal resistance, which limits the lattice thermal conductivity x~. We present a summary of the available experimental data on 8", ", emphasizing uncertainties and contrasting results from different types of experiments. Methods of obtaining better data are suggested. We show that the available data are in fair agreement with a simple theoretical estimate lim(T~0) 8', "(T/8~) = 0.42 0, '" N X(Kcm/W), where 0, is the atomic volume in A3, N is the Fermi-energy density of states (1 spin) in states/eV, and P is the electron-phonon mass enhancement. The fact that most of the experimental points fall below this estimate is probably the result of anisotropy and mode dependence of the electronphonon coupling.
First principles theory of the lattice thermal conductivity of semiconductors
2009
Using density functional perturbation theory and a full solution of the linearized phonon Boltzmann transport equation (BTE), a parameter-free theory of semiconductor thermal properties is developed. The approximations and shortcomings of previous approaches to thermal conductivity calculations are investigated. The use of empirical interatomic potentials in the BTE approach is shown to give poor agreement with measured values of thermal conductivity. By using the adiabatic bond charge model, the importance of accurate descriptions of phonon dispersions is highlighted. The extremely limited capacity of previous theoretical techniques in the realm of thermal conductivity prediction is highlighted; this is due to a dependence on adjustable parameters. Density functional perturbation theory is coupled with an iterative solution to the full Boltzmann transport equation creating a theoretical construct where thermal conductivity prediction becomes possible. Validation of the approach is ...
Thermal Conductivity and Phonon Engineering in Low-Dimensional Structures
1998
The use of first principles methods based on density functional theory to investigate novel thermoelectric materials is illustrated for several empty and filled skutterudite compounds, including CoSb 3 , C0P3, La(Fe,Co) 4 Sbi 2 and La(Fe,Co)P 12 . Band structures and their relationship to transport properties especially as regards optimization of thermoelectric properties is discussed. Phonon models constructed from calculations and existing experimental data for CoSb 3 are presented. These have been extended to the filled skutterudites, particularly LaFe 4 Sbi2 using additional first principles calculations to fix the La related parameters in the model. This model allows an interpretation of neutron scattering data as well as an understanding of the low frequency phonon modes that transport heat in these compounds.