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.

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Nanoscale thermal transport

We review the physical properties of diluted magnetic semiconductors (DMS) of the type AII1−xMnxBVI (e.g., Cd1−xMnxSe, Hg1−xMnxTe). Crystallographic properties are discussed first, with emphasis on the common structural features which these materials have as a result of tetrahedral bonding. We then describe the band structure of the AII1−xMnxBVI alloys in the absence of an external magnetic field, stressing the close relationship of the sp electron bands in these materials to the band structure of the nonmagnetic AIIBVI ‘‘parent’’ semiconductors. In addition, the characteristics of the narrow (nearly localized) band arising from the half‐filled Mn 3d5 shells are described, along with their profound effect on the optical properties of DMS. We then describe our present understanding of the magnetic properties of the AII1−xMnxBVI alloys. In particular, we discuss the mechanism of the Mn++‐Mn++ exchange, which underlies the magnetism of these materials; we present an analytic formulation for the magnetic susc...

Diluted magnetic semiconductors

We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties---optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

The theory and properties of randomly disordered crystals and related physical systems

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Infrared detectors: status and trends

Publisher Summary This chapter discusses statistical exchange-correlation in the self-consistent field. There are two sides to a self-consistent field calculation: the determination of the potential and the solution of Schrodinger's equation for the one-electron problem. The solution of Schrodinger's equation has fortunately advanced far enough through the application of the electronic digital computer so that it can be regarded for most purposes as being a standardized technique. The main point of the method of Gaspar, Kohn, and Sham is that they derive the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonian for the ground state. The approximate Hamiltonian has many important and valuable features that are described in the chapter.

Statistical Exchange-Correlation in the Self-Consistent Field

The performance characteristics of type‐II InAs/InxGa1−xSb superlattices for long and very long‐wave infrared detection are discussed. This system promises benefits in this wavelength range over conventional technology based on Hg1−xCdxTe, in part because of suppressed band‐to‐band Auger recombination rates which lead to improved values of detectivity. The formalism for calculating Auger rates in superlattices is developed and the physical origin of Auger suppression in these systems is discussed. Accurate K⋅p band structures are used to obtain radiative, electron–electron, hole–hole, and band‐to‐band Auger rules, as well as shallow trap level assisted Auger recombination rates for photodiodes. Theoretical limits for high temperature operation of ideal photovoltaic detectors are presented and compared with HgCdTe.

http://frg.physics.uiowa.edu/publications/1995_016.pdf

Long wavelength InAs/InGaSb infrared detectors: Optimization of carrier lifetimes

The coherent-potential approximation (CPA) is extended to study general band shapes and systems having orbital degeneracy. This permits its application to realistic systems, in particular the $\mathrm{Ni}\mathrm{Cu}$ alloys. The effects of alloying on a highly asymmetric model density of states characteristic of some of the features of the density of states in fcc transition metals are considered in detail. A model Hamiltonian for paramagnetic $\mathrm{Ni}\mathrm{Cu}$ is constructed using a basis of orthogonalized plane waves and tight-binding $d$ functions. Orbital degeneracy and hybridization are treated as in paramagnetic Ni. Effects of alloying are assumed to be restricted to the diagonal elemensts of the $d\ensuremath{-}d$ block. The model is applicable to the Ni-rich alloys, as is the approximation used to obtain simple solutions of the full CPA equations. The results are consistent with recent photoemission data on $\mathrm{Ni}\mathrm{Cu}$, and with the "minimum polarity" hypothesis used by Lang and Ehrenreich. They are incompatible with the rigid-band model because the scattering potential of the random alloy is strong compared to the peak widths. Rather than a rigid shift of the density of states, the calculated concentration dependence shows that the main peaks remain stationary while changing magnitude and shape. Decomposition of the total density of states into Ni and Cu contributions confirms that, for the expected position of the Fermi level, the $d$ holes are located primarily on Ni sites.

Paramagnetic Ni Cu Alloys: Electronic Density of States in the Coherent-Potential Approximation

The renormalized-atom approach, first used by Chodorow, is shown to yield quantitative estimates of some of the essential potential-dependent parameters characterizing transition-metal band structures on the basis of essentially atomic considerations. These are the position ${\ensuremath{\Gamma}}_{1}$ of the conduction-band minimum, the mean $d$-band energy, the energies associated with $d$-band extrema, and the degree of $s\ensuremath{-}d$ hybridization as defined within the Heine-Hubbard pseudopotential schemes. The estimates of ${\ensuremath{\Gamma}}_{1}$ and the $d$-band extrema utilize "renormalized-atom" band potentials within the Wigner-Seitz cell in which the interelectronic exchange is taken into account without resort to the ${\ensuremath{\rho}}^{\frac{1}{3}}$ approximation and incorporate the appropriate boundary conditions at the Wigner-Seitz radius ${r}_{\mathrm{WS}}$. The results have comparable accuracy with those obtained from augmented-plane-wave calculations employing the same crystal potential within the muffin-tin approximation. The band results are qualitatively similar to those obtained using more conventional ${\ensuremath{\rho}}^{\frac{1}{3}}$ potentials. The Wigner-Seitz viewpoint is thereby seen to be useful in obtaining quantitative results for certain high-symmetry points in $k$ space aside from ${\ensuremath{\Gamma}}_{1}$ with far less computational effort. In addition, the present scheme may provide a better starting point for dealing with $d\ensuremath{-}d$ exchange-correlation effects. Also discussed are a number of features general to the problem of constructing adequate transition-metal crystal potentials, in particular, how to deal with nonintegral $d$- and conduction-electron counts per atom, and configuration and/or multiplet averaging.

Renormalized Atoms and the Band Theory of Transition Metals

The effects of alloy disorder on the electronic structure of ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$ are examined with the use of the coherent-potential approximation. An empirical tight-binding scheme, including spin-orbit effects, is employed. The choice of parameters is given special emphasis. A new HgTe band structure is obtained. Alloying effects are illustrated by quasiparticle spectral densities, total and projected densities of states, and self-energy corrections to the virtual-crystal energy bands. Strong cation $s$ scattering results in significant damping far from the band edges and accounts for the split-band behavior seen in photoemission experiments. The unusual bowing effects of the fundamental band gap and that associated with the ${E}_{1}$ transition are well explained. The weak scattering regime is shown to apply near the band edges. The electron mobility due to alloy scattering is large and does not appear to limit the observed magnitude.

Henry Ehrenreich

Papers

Long wavelength InAs/InGaSb infrared detectors: Optimization of carrier lifetimes

Paramagnetic Ni Cu Alloys: Electronic Density of States in the Coherent-Potential Approximation

Renormalized Atoms and the Band Theory of Transition Metals

Electronic structure of Hg 1-x Cd x Te

Single-site approximations in the electronic theory of liquid metals