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Vibrational Properties of Semiconductors, and Electron-Phonon Interactions

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Fundamentals of Semiconductors

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Abstract

We will start the discussion of the vibrational properties of semiconductors by reviewing the theory of the dynamics of a crystalline lattice. The Hamilto-nian describing a perfect crystal has already been given in (2.1). We note that the electrons have been separated into two groups. The core electrons are assumed to move rigidly with the nucleus to form what has been referred to as the ion. The valence electrons interact with these ions via the pseudopotentials. The part Hamiltonian in (2.1) which involves the nuclear motions is given by

$$ {H_{ion}}({R_1},...,{R_n}) = \sum\limits_j {\frac{{P_j^2}}{{2{M_j}}} + \sum\limits_{j,j'} {^,} \frac{1}{2}\frac{{{Z_j}{Z_{j'}}{e^2}}}{{\left| {{R_j} - {R_{j'}}} \right|}} - \sum\limits_{i.j} {\frac{{{Z_j}{e^2}}}{{\left| {{r_i} - {R_j}} \right|}}} } $$
((3.1))

, where R j, P j, Z j and M j are, respectively, the nuclear positions, momentum, charge, and mass, r t is the position of the electron and Σ’ means summation over pairs of indices j and j’ where j is not equal to j’.

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Authors and Affiliations

  1. Department of Physics, University of California, 94720-7300, Berkeley, CA, USA

    Professor Dr. Peter Y. Yu

  2. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569, Stuttgart, Germany

    Professor Dr., Dres. h.c. Manuel Cardona

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  1. Professor Dr. Peter Y. Yu
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  2. Professor Dr., Dres. h.c. Manuel Cardona
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© 1996 Springer-Verlag Berlin Heidelberg

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Yu, P.Y., Cardona, M. (1996). Vibrational Properties of Semiconductors, and Electron-Phonon Interactions. In: Fundamentals of Semiconductors. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03313-5_3

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  • DOI: https://doi.org/10.1007/978-3-662-03313-5_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61461-6

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