Publisher Summary This chapter reviews the thermal conductivity of nonmetallic crystals at temperatures comparable to or higher than the Debye temperature. It deals with the intrinsic behavior of such pure crystals at high temperatures. In such crystals, the dominant carriers of thermal energy are phonons and the dominant scattering mechanism to be considered is the intrinsic phonon–phonon scattering. This is a small section of the much larger problem of the thermal conductivity of nonmetallic solids and clearly it neglects possible heat transport by photons, charge carriers, polarons, and magnons. It also neglects other possible phonon scattering mechanisms such as isotopes, impurities, vacancies, charge carriers, dislocations, grain boundaries, and crystal boundaries. It presents the absolute value of the thermal conductivity, K, as determined by phonon–phonon scattering, the temperature dependence of K, the volume dependence of K, the change in K upon melting, and the minimum value of K. The chapter discusses a composite curve for the thermal conductivity versus temperature of pure KCl measured at a constant pressure of, say, one atmosphere.

The Thermal Conductivity of Nonmetallic Crystals

We have measured the temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{n}$. The full widths at half maximum of the Raman lines, extrapolated to zero temperature, are 1.24\ifmmode\pm\else\textpm\fi{}0.07, 0.75\ifmmode\pm\else\textpm\fi{}0.03, and 0.81\ifmmode\pm\else\textpm\fi{}0.15 ${\mathrm{cm}}^{\ensuremath{-}1}$ for Si, Ge, and $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{n}$, respectively. The reliability of the data obtained allows a critical examination of the theoretical calculations published so far. We show that the model assuming the decay of the Raman phonon into two acoustical phonons belonging to the same branch, first proposed by Klemens, does not represent adequately the temperature dependence of the Raman linewidth. The most important decay channels are shown to be combinations of optical and acoustical phonons. However, the more complete calculation by Cowley, which involves all possible decay channels, gives very large zero-temperature linewidths. We show that this arises mainly from the poor description of the phonon dispersion curves by the shell model used by Cowley, and that a better agreement between theory and experiment is to be expected by repeating the calculation with Weber's adiabatic bond-charge model.

Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and α − S n : Anharmonic effects

The isotope effect on the lattice thermal conductivity for group IV and group III-V semiconductors is calculated using the Debye-Callaway model modified to include both transverse and longitudinal phonon modes explicitly. The frequency and temperature dependences of the normal and umklapp phonon-scattering rates are kept the same for all compounds. The model requires as adjustable parameters only the longitudinal and transverse phonon Gr\"uneisen constants and the effective sample diameter. The model can quantitatively account for the observed isotope effect in diamond and germanium but not in silicon. The magnitude of the isotope effect is predicted for silicon carbide, boron nitride, and gallium nitride. In the case of boron nitride the predicted increase in the room-temperature thermal conductivity with isotopic enrichment is in excess of 100%. Finally, a more general method of estimating normal phonon-scattering rate coefficients for other types of solids is presented.

Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors

Since the end of the cold war, macroscopic amounts of separated stable isotopes of most elements have been available ``off the shelf'' at affordable prices. Using these materials, single crystals of many semiconductors have been grown and the dependence of their physical properties on isotopic composition has been investigated. The most conspicuous effects observed have to do with the dependence of phonon frequencies and linewidths on isotopic composition. These affect the electronic properties of solids through the mechanism of electron-phonon interaction, in particular, in the corresponding optical excitation spectra and energy gaps. This review contains a brief introduction to the history, availability, and characterization of stable isotopes, including their many applications in science and technology. It is followed by a concise discussion of the effects of isotopic composition on the vibrational spectra, including the influence of average isotopic masses and isotopic disorder on the phonons. The final sections deal with the effects of electron-phonon interaction on energy gaps, the concomitant effects on the luminescence spectra of free and bound excitons, with particular emphasis on silicon, and the effects of isotopic composition of the host material on the optical transitions between the bound states of hydrogenic impurities.

Isotope effects on the optical spectra of semiconductors

This paper presents a Monte Carlo simulation scheme to study the phonon transport and the thermal conductivity of nanocomposites. Special attention has been paid to the implementation of periodic boundary condition in Monte Carlo simulation. The scheme is applied to study the thermal conductivity of silicon germanium (Si-Ge) nanocomposites, which are of great interest for high-efficiency thermoelectric material development. The Monte Carlo simulation was first validated by successfully reproducing the results of (two-dimensional) nanowire composites using the deterministic solution of the phonon Boltzmann transport equation reported earlier and the experimental thermal conductivity of bulk germanium, and then the validated simulation method was used to study (three-dimensional) nanoparticle composites, where Si nanoparticles are embedded in Ge host. The size effects of phonon transport in nanoparticle composites were studied, and the results show that the thermal conductivity of nanoparticle composites can be lower than that of the minimum alloy value, which is of great interest to thermoelectric energy conversion. It was also found that randomly distributed nanopaticles in nanocomposites rendered the thermal conductivity values close to that of periodic aligned patterns. We show that interfacial area per unit volume is a useful parameter to correlate the size effect of thermal conductivity in nanocomposites. The key for the thermal conductivity reduction is to have a high interface density where nanoparticle composites can have a much higher interface density than the simple ID stacks, such as superlattices. Thus, nanocomposites further benefit the enhancement of thermoelectric performance in terms of thermal conductivity reduction. The thermal conductivity values calculated by this work qualitatively agrees with a recent experimental measurement of Si-Ge nanocomposites.

Modeling the Thermal Conductivity and Phonon Transport in Nanoparticle Composites Using Monte Carlo Simulation

Phonon dispersion relations in Ge have been measured at 80 \ifmmode^\circ\else\textdegree\fi{}K for all principal symmetry directions and on some lines at the boundary of the Brillouin zone. The measurements were performed by neutron inelastic scattering using a three-axis crystal spectrometer. In order to achieve maximum accuracy, care was taken to reduce resolution widths as far as possible. In general, the estimated uncertainties of the measured phonon frequencies range from 0.3% to 0.5% for optical and from 0.3% to 1% for acoustic phonons. Frequencies of 238 phonons are tabulated and phonon linewidths are given for the symmetry directions.

G. Nilsson

Papers

Phonon Dispersion Relations in Ge at 80 °K