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

Electron transport experiments on two lateral quantum dots coupled in series are reviewed. An introduction to the charge stability diagram is given in terms of the electrochemical potentials of both dots. Resonant tunneling experiments show that the double dot geometry allows for an accurate determination of the intrinsic lifetime of discrete energy states in quantum dots. The evolution of discrete energy levels in magnetic field is studied. The resolution allows one to resolve avoided crossings in the spectrum of a quantum dot. With microwave spectroscopy it is possible to probe the transition from ionic bonding (for weak interdot tunnel coupling) to covalent bonding (for strong interdot tunnel coupling) in a double dot artificial molecule. This review is motivated by the relevance of double quantum dot studies for realizing solid state quantum bits.

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Electron transport through double quantum dots

Annals of physics

Theoretical models of Schottky-barrier height formation are reviewed. A particular emphasis is placed on the examination of how these models agree with general physical principles. New concepts on the relationship between interface dipole and chemical bond formation are analyzed, and shown to offer a coherent explanation of a wide range of experimental data.

Recent advances in Schottky barrier concepts

In the quest for higher performance, the dimensions of field-effect transistors (FETs) continue to decrease. However, the reduction in size of FETs comprising 3D semiconductors is limited by the rate at which heat, generated from static power, is dissipated. The increase in static power and the leakage of current between the source and drain electrodes that causes this increase, are referred to as short-channel effects. In FETs with channels made from 2D semiconductors, leakage current is almost eliminated because all electrons are confined in atomically thin channels and, hence, are uniformly influenced by the gate voltage. In this Review, we provide a mathematical framework to evaluate the performance of FETs and describe the challenges for improving the performances of short-channel FETs in relation to the properties of 2D materials, including graphene, transition metal dichalcogenides, phosphorene and silicene. We also describe tunnelling FETs that possess extremely low-power switching behaviour and explain how they can be realized using heterostructures of 2D semiconductors. Field-effect transistors (FETs) with semiconducting channels made from 2D materials are known to have fewer problems with short-channel effects than devices comprising 3D semiconductors. In this Review, a mathematical framework to evaluate the performance of FETs is outlined with a focus on the properties of 2D materials, such as graphene, transition metal dichalcogenides, phosphorene and silicene.

Two-dimensional semiconductors for transistors

This is a study of simple kinetic models of open systems, in the sense of systems that can exchange conserved particles with their environment. The system is assumed to be one dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville---von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time reversible, exponentially growing (unphysical) solutions are introduced into the time dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and its continuum formulations, are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.

Boundary conditions for open quantum systems driven far from equilibrium

Wigner-function model of a resonant-tunneling semiconductor device.

We present a refined model for the prediction of the energy-band lineup at an abrupt semiconductor heterojunction. The position of the energy bands with respect to the electrostatic potential is calculated by a self-consistent pseudopotential,for the bulk semiconductors. The lineup of the electrostatic potentials is then calculated from an ionic model in which the ionic charges are determined by the electronegativities of the atomic species. The resulting band lineups are independent of the crystallographic orientation of the heterojunction. They are also generally consistent with experimental data.

Theory of the energy-band lineup at an abrupt semiconductor heterojunction

We present results of the fabrication and investigation of totally spatially localized crystalline structures. Low temperature photoluminescence exhibits structure that is best explained by a bottleneck for hole energy loss. This bottleneck is believed to be a direct consequence of the modification of the band structure by the fabrication‐imposed potential and is believed to be the first evidence for total spatial quantization in a fabricated heterojunction system.

Spatial quantization in GaAs–AlGaAs multiple quantum dots

Quantitative simulation of an InGaAs/InAlAs resonant tunneling diode is obtained by relaxing three of the most widely employed assumptions in the simulation of quantum devices. These are the single band effective mass model (parabolic bands), Thomas-Fermi charge screening, and the Esaki-Tsu 1D integral approximation for current density. The breakdown of each of these assumptions is examined by comparing to the full quantum mechanical calculations of self-consistent quantum charge in a multiband basis explicitly including the transverse momentum.

William R. Frensley

Papers

Boundary conditions for open quantum systems driven far from equilibrium

Wigner-function model of a resonant-tunneling semiconductor device.

Theory of the energy-band lineup at an abrupt semiconductor heterojunction

Spatial quantization in GaAs–AlGaAs multiple quantum dots

Quantitative simulation of a resonant tunneling diode