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Phonon-Induced Thermal Properties

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Semiconductor Physics

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.

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Notes

  1. 1.

    Although the specific heat is measured more easily for constant pressure C P , the difference between C V and C P 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 V m 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 α V is observed at very low temperatures (see end of Sect. 2.2 in this chapter).

  4. 4.

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

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Böer, K.W., Pohl, U.W. (2018). Phonon-Induced Thermal Properties. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-69150-3_5

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