G. D. Mahan

Nanoscale thermal transport

Rapid progress in the synthesis and processing of materials with structure on nanometer length scales has created a demand for greater scientific understanding of thermal transport in nanoscale devices, individual nanostructures, and nanostructured materials. This review emphasizes developments in experiment, theory, and computation that have occurred in the past ten years and summarizes the present status of the field. Interfaces between materials become increasingly important on small length scales. The thermal conductance of many solid–solid interfaces have been studied experimentally but the range of observed interface properties is much smaller than predicted by simple theory. Classical molecular dynamics simulations are emerging as a powerful tool for calculations of thermal conductance and phonon scattering, and may provide for a lively interplay of experiment and theory in the near term. Fundamental issues remain concerning the correct definitions of temperature in nonequilibrium nanoscale systems. Modern Si microelectronics are now firmly in the nanoscale regime—experiments have demonstrated that the close proximity of interfaces and the extremely small volume of heat dissipation strongly modifies thermal transport, thereby aggravating problems of thermal management. Microelectronic devices are too large to yield to atomic-level simulation in the foreseeable future and, therefore, calculations of thermal transport must rely on solutions of the Boltzmann transport equation; microscopic phonon scattering rates needed for predictive models are, even for Si, poorly known. Low-dimensional nanostructures, such as carbon nanotubes, are predicted to have novel transport properties; the first quantitative experiments of the thermal conductivity of nanotubes have recently been achieved using microfabricated measurement systems. Nanoscale porosity decreases the permittivity of amorphous dielectrics but porosity also strongly decreases the thermal conductivity. The promise of improved thermoelectric materials and problems of thermal management of optoelectronic devices have stimulated extensive studies of semiconductor superlattices; agreement between experiment and theory is generally poor. Advances in measurement methods, e.g., the 3ω method, time-domain thermoreflectance, sources of coherent phonons, microfabricated test structures, and the scanning thermal microscope, are enabling new capabilities for nanoscale thermal metrology.

Thermoelectric materials: New approaches to an old problem

Thermoelectrics is an old field. In 1823, Thomas Seebeck discovered that a voltage drop appears across a sample that has a temperature gradient. This phenomenon provided the basis for thermocouples used for measuring temperature and for thermoelectric power generators. In 1838, Heinrich Lenz placed a drop of water on the junction of metal wires made of bismuth and antimony. Passing an electric current through the junction in one direction caused the water to freeze, and reversing the current caused the ice to quickly melt; thus thermoelectric refrigeration was demonstrated (figure 1).

Nanoscale thermal transport. II. 2003–2012

A diverse spectrum of technology drivers such as improved thermal barriers, higher efficiency thermoelectric energy conversion, phase-change memory, heat-assisted magnetic recording, thermal management of nanoscale electronics, and nanoparticles for thermal medical therapies are motivating studies of the applied physics of thermal transport at the nanoscale. This review emphasizes developments in experiment, theory, and computation in the past ten years and summarizes the present status of the field. Interfaces become increasingly important on small length scales. Research during the past decade has extended studies of interfaces between simple metals and inorganic crystals to interfaces with molecular materials and liquids with systematic control of interface chemistry and physics. At separations on the order of ∼1 nm, the science of radiative transport through nanoscale gaps overlaps with thermal conduction by the coupling of electronic and vibrational excitations across weakly bonded or rough interface...

Theory of conduction in ZnO varistors

A theory is presented which quantitatively accounts for the important features of conduction in ZnO‐based metal‐oxide varistors. This theory has no adjustable parameters. Using the known values of the ZnO band gap, donor concentration n0, and low‐voltage varistor leakage‐current activation energy, we predict a varistor breakdown voltage of ?3.2 V/grain boundary for n0=1017 carriers cm−3 and T=300 °K. This compares well with measurements on a single grain‐grain junction. The highly nonlinear varistor conduction derives from electron tunneling ’’triggered’’ by hole creation in the ZnO when the conduction band in the grain interior drops below the top of the valence band at the grain interface. The theory predicts coefficients of nonlinearity α=d (lnI)/d (lnV) as high as 50, or even 100.

Collective vibrational modes of adsorbed CO

The interpretation, in terms of dipole interactions, of the dependence on coverage of the stretching frequency of CO adsorbed of metal sufaces is re‐examined. We take into account substrate image effects and dielectric screening of the adsorbed layer. We also provide a theory of the statistical fluctuations in random, partially filled layers. The dipole interactions provide a frequency shift of about 10 cm−1, which is only about one third of that usually observed.

Minimum Thermal Conductivity of Superlattices

The phonon thermal conductivity of a multilayer is calculated for transport perpendicular to the layers. There is a crossover between particle transport for thick layers to wave transport for thin layers. The calculations show that the conductivity has a minimum value for a layer thickness somewhat smaller then the mean free path of the phonons.

Intrinsic defects in ZnO varistors

Theoretical calculations are presented for equilibrium concentrations of zinc and oxygen vacancies in ZnO. Results are presented at the sintering temperature, and also at room temperature. Theoretical calculations of reaction constants show that the intrinsic donor is the oxygen vacancy, rather than the zinc interstitial. The depletion of vacancies in the surface region, as the ZnO is cooled from the sintering temperature, is also calculated. Homojunction effects which are caused by such depletion are shown to be small.

Energy gap in Si and Ge: Impurity dependence

The energy gap in silicon and germanium is calculated as a function of the concentration of donor impurities. The results are compared with the available data from optical experiments and devices. Previous theories are critically reviewed.

Dynamical simulations of nonequilibrium processes — Heat flow and the Kapitza resistance across grain boundaries

We report molecular dynamics simulations of nonequilibrium heat flow in a solid system in the local-equilibrium or hydrodynamic approximation and demonstrate that local equilibrium can be achieved in small numbers of atomic layers over long simulation runs. From the dynamical simulations, we calculate the thermal boundary (Kapitza) resistance that arises from heat flow across Si grain boundaries and compare with the traditional approach based on calculating the transmission and reflection of harmonic phonons at the grain boundary.

Figure of merit for thermoelectrics

Theoretical calculations are presented for the figure of merit Z in thermoelectrics. The maximum values of Z are obtained in semiconductors which are doped so that the chemical potential is near the band edge. The highest Z is related to the B parameter of Chasmar and Stratton [J. Electron. Control 7, 52 (1959)].