Phonon Transport and Heat Flow

Phonon Transport and Heat Flow

DOI: 10.4018/978-1-5225-2312-3.ch007
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1. Overview And Chapter Objectives

The transport of heat energy is an old topic in physics, dated back to Joseph Fourier (1822). Different kinds of heat carriers have been proposed to explain this process, namely: molecules, electrons, phonons and photons. In this chapter, we concentrate our attention on the heat transport by phonons.

Phonons are quantized vibrations of the crystal lattice atoms. They are like electrons or photons (light particles), in that they carry energy. Phonons are actually the main heat carriers in semiconductors and insulators. Heat flows from the hot side to the cold side of a system whenever it is not in thermal equilibrium and temperature distribution is not uniform. Researchers are trying to answer fundamental questions about how phonons transport heat.

The energy transport and exchange between electrons and phonons in a crystalline solid is a vital topic in solid state physics. The interest of this topic has been raised by the miniaturization of electronic devices, where the heat removal imposes many restrictions on the development of semiconductor nanodevices. In fact, the heat transport and evacuation is related to the performance and the reliability issues, in a wide class of semiconductors devices, including MOSFET’s and lasers. In addition, the thermoelectric applications motivate the studies of thermal transport in nanostructures and the emerging phononic nanodevices.

For long time, the heat transfer by conduction, in solid-state devices has been studied on the basis of Fourier’s diffusion model (Q=-kth∇T). Actually, the heat is carried predominantly by phonons in dielectrics and semiconductors. The relationship between the phonon mean free path of heat transfer and the device length scale determines whether thermal transport follows the classical thermal diffusion model or not. It is found that the optical and high frequency acoustic phonons provide the main contributions to the specific heat of bulk materials, where the mean free path of phonons is much smaller than the device length scale. However, for any length scale there will be some phonons of low enough frequency that propagate ballistically (without scattering) rather than diffusively (with scattering).

After a review of the basic physics and thermodynamics of heat and phonons we present the phonon transport theory. The phonon transport parameters such as thermal conductivity are introduced from the atomic-level properties using semiclassical and quantum approaches. We present the semiclassical and quantum schemes as well as phenomenological models, and examine their range of applications. In particular, we discuss the validity of different models of thermal conductivity for nanostructures and nanodevices. Figure 1 recapitulates the hierarchy of phonon transport approaches, which have been presented so far in the literature. Microscopic approaches may be quantum, semiclassical or based on molecular dynamics (MD). The microscopic semiclassical models, such as the Peierls-Boltzmann transport equation (phonon BTE) and Lattice Monte-Carlo simulation, can capture quasi-ballistic phonon transport.

Figure 1.

Hierarchy of phonon and heat transport models

Upon completion of this Chapter, the readers and students will:

  • Review the notions of lattice temperature and heat transfer mechanisms

  • Review the basics of lattice vibrations and phonon waves

  • Describe the phonon scattering mechanisms and how they affect the heat conductivity of a semiconductor or insulator

  • Understand the phonon transport mechanisms (diffusive, hydrodynamic and ballistic), and how they contribute to the thermal properties of solids

  • Understand and know how and when to employ the phonon transport models, with molecular dynamics (MD) methods as well as semiclassical (phonon BTE) and quantum approaches (NEGF).

  • Understand the phonon transport in low-dimensional structures, such as carbon nanotubes and graphene ribbons

  • Understand and appreciate the concepts of the emerging phononic devices.

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