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Excitations in One-Component Carrier Gases

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Book cover Semiconductor Optics 1

Part of the book series: Graduate Texts in Physics ((GTP))

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Abstract

The linear optical properties of heavily doped semiconductors are strongly influenced by the plasma of free carriers present in this samples. This includes of course the (degenerate) occupation of band states as well as correlation effects like collective excitations. We will address the implications of plasmons and pair excitations in the carrier gas and the description of the related optical properties in the Drude–Lorentz model. We illustrate the optical properties related to surface plasmons and of plasmon-phonon mixed states both, in bulk and low-dimensional semiconductors. We close with a discussion of prominent correlation effects like the Burstein–Moss shift and the Fermi-edge singularity.

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Author information

Authors and Affiliations

  1. Institute of Applied Physics, Karlsruhe Institute of Technology, Karlsruhe, Baden-Württemberg, Germany

    Heinz Kalt & Claus F. Klingshirn

Authors
  1. Heinz Kalt
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  2. Claus F. Klingshirn
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Correspondence to Heinz Kalt .

Problems

Problems

19.1

Calculate the plasmon energy \(\hbar \omega ^{0}_{\text {Pl}}\) for a typical three-dimensional semiconductor \((m_{\text {e}} = 0.1m_{0})\) and \(n=10^{16}\), \(10^{17}\) and \(10^{18}\) cm\(^{-3}\). Compare with the eigenenergies of optical phonons.

19.2

Calculate \(\hbar \omega ^0_{\text {Pl}}\) for a metal \((n\thickapprox 10^{22}- 10^{23}\)cm\(^{3})\). Using the knowledge of Chap. 7, consider which value should be taken for the dielectric “constant” \(\varepsilon \)?

19.3

What is the origin of the color of some metals like gold or copper? Remember that there are, apart from plasmons, interband-transitions in metals.

19.4

Why are radio waves in the short wave range (KW) reflected by the upper layers of the atmosphere but not ultrashort waves (UKW)?

19.5

Why are surface plasmons important for the spectral efficiency of a metal- covered diffraction grating?

19.6

Make a sketch of the dielectric function of plasmon–phonon mixed states for \(\omega _{{\text {Pl}}}^0 >\omega _0 \).

19.7

Calculate the density of electrons at which \(\hbar \omega _{\text {PL}} = \hbar \varOmega _{\text {LO}}\) for ZnO and InAs. Up to which temperatures are the electron gases degenerate?

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Kalt, H., Klingshirn, C.F. (2019). Excitations in One-Component Carrier Gases. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_19

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