Heat under the microscope

Abstract

[Introduction] Recent advances in computational and spectroscopic tools offer new insights into the nature of thermal conduction at ever-finer length scales and ways to control it. Heat conduction is familiar to us all and yet requires a wide range of physics—statistical mechanics, crystallography, and quantum mechanics among them—to fully explain. At the macroscale, heat conduction can be described as a diffusion process in which energy moves along a temperature gradient. The heat flux dissipated by the gradient depends on a material property, the thermal conductivity, as described by the constitutive relation, Fourier’s law. The heat equation, which is derived from Fourier’s law and the conservation of energy, describes the distribution of temperature over space and time.

Typically, the heat equation is assumed to be the end of the story for thermal conduction. However, the macroscopic theory leaves some fundamental questions unanswered. For example, why is diamond an exceptional thermal conductor, whereas gallium arsenide, a material with the same crystal structure, is only an average one? Lattice vibrations have long been understood as being responsible for heat conduction in a solid, but among the broad spectrum of the vibrational modes, which are primarily responsible for heat conduction? And what are the typical propagation lengths of those vibrations?

The answers to such questions are of considerable importance as electronic components become ever smaller and faster. In many applications—including LED lighting, high-power transistors, ultrasensitive radiation detectors, and thermoelectric waste-heat recovery—a microscopic view of thermal transport is essential. To list just one example, the rise in temperature near the active region of a transistor can be significantly higher—by tens of kelvin—than predicted by Fourier’s law, and that discrepancy affects the performance and reliability of devices ranging from smartphones to power amplifiers.