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Phonon-Induced Thermal Properties

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Semiconductor Physics

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Abstract

Phonons are responsible for all thermal properties of a solid, such as its heat content and transport. The anharmonic part of lattice oscillations causes thermal expansion. All these are integral contributions of the phonon spectrum; only at low temperatures, where part of the spectrum can be frozen-out, do they become partially spectrum selective. Thermal conductivity is determined by various mechanisms of phonon scattering. Most important are phonon-phonon and disordered-induced scattering. In nanostructures scattering at boundaries is dominant.

Karl W. Böer: deceased.

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Notes

  1. 1.

    Although the specific heat is measured more easily for constant pressure CP, the difference between CV and CP is very small for solids and is given by

    $$ {C}_P-{C}_V=\frac{9{\alpha}^2T{V}_m}{\kappa } $$
    (1)

    where α is the thermal expansion coefficient, κ is the isothermal compressibility, and Vm is the molar volume.

  2. 2.

    The specific heat is given here in Ws/(mol K) and should be distinguished from the values often given in tables in units of Ws/(cm3K) or Ws/(gK).

  3. 3.

    Exceptions like H2O or In are caused by rather unusual changes in the atomic structure of the solid. (Were it not for these changes in H2O, lakes would freeze from the bottom up.) Another important anomaly of αV is observed at very low temperatures (see end of Sect. 2.2 in this chapter).

  4. 4.

    In the Casimir model, phonons travel ballistically and scattering occurs only at the boundaries of the nanostructure; these are considered as perfect “phonon black bodies.”

  5. 5.

    The dominant phonon wavelength is in the range of \( {\Lambda}_{\mathrm{dom}}=1.48{v}_s\hslash /(kT); \) see Klitsner and Pohl 1987.

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  1. Institut für Festkörperphysik, EW5-1, Technische Universität Berlin, Berlin, Germany

    Udo W. Pohl

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Böer, K.W., Pohl, U.W. (2023). Phonon-Induced Thermal Properties. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-18286-0_5

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