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Semiconductor Physics pp 1–30Cite as

Carrier Scattering at High Electric Fields

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Abstract

At high electric fields the scattering of carriers is significantly influenced by carrier heating. Usually scattering is increased and counteracts an enhanced accumulation of carrier energy from the field. Such increased scattering is observed for interaction with phonons, causing a decrease in mobility: first mostly from acoustical scattering and at higher fields from LO-phonon scattering. The drift velocity is thereby limited to values close to the thermal carrier velocity. The deformed carrier distribution can be approximated by a Boltzmann distribution, assuming a carrier temperature elevated above the lattice temperature. Above the energy of longitudinal optical phonons the distribution is skewed substantially, and a description of the distribution function and carrier mobility by a Fourier series is more appropriate. Also numerical solutions of transport problems are then advantageous.

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Notes

  1. 1.

    This sublinearity occurs as long as no run-away currents preceding the dielectric breakdown are initiated (Yu and Cardona 1996). The run-away current regime will be discussed in Sect. 2.2 of chapter “Carrier Generation”.

  2. 2.

    The parameters vsat and β are obtained from curve-fitting, depending on materials; for Si they are (Canali et al. 1975) for electrons vsat n = 1.53·109×T -0.87 (cm/s), βn = 2.57·10−2×T 0.66 (cm/s), and for holes vsat p = 1.62·108×T -0.52 (cm/s), βp = 0.46×T 0.17 (cm/s), with the temperature given in K.

  3. 3.

    For example, conductivity measurements rely on carrier densities obtained from low-field measurements using Hall-effect data; time-of-flight techniques can hardly exclude shallow-level trapping.

  4. 4.

    Compare to the high-field domains in superlattices discussed in Sect. 2.3.2 of chapter “Carrier Transport in Low-Dimensional Semiconductors”.

  5. 5.

    This approximation is no longer acceptable for electrons exceeding the energy of LO phonons, as the tail of the distribution becomes substantially deformed, see Sect. 2.2.1 in chapter “Carrier Generation”.

  6. 6.

    G is the Green function and W is the screened Coulomb potential; GW is employed for calculating the electron exchange-correlation interactions – see also Sects. 2.1.7 and 2.2.3 of chapter “Quantum Mechanics of Electrons in Crystals”.

  7. 7.

    The effective mass in one of the four satellite minima is 0.4 m0; the density-of-state mass is hence (0.43/2 × 4)2/3 m0 = 1.01 m0).

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Authors and Affiliations

  1. Naples, FL, USA

    Karl W. Böer

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

    Udo W. Pohl

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Böer, K.W., Pohl, U.W. (2017). Carrier Scattering at High Electric Fields. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_24-2

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    Carrier Scattering at High Electric Fields
    Published:
    12 June 2022

    DOI: https://doi.org/10.1007/978-3-319-06540-3_24-4

  2. Carrier Scattering at High Electric Fields
    Published:
    26 March 2020

    DOI: https://doi.org/10.1007/978-3-319-06540-3_24-3

  3. Carrier Scattering at High Electric Fields
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    28 September 2017

    DOI: https://doi.org/10.1007/978-3-319-06540-3_24-2

  4. Original

    Carrier Scattering at High Electric Fields
    Published:
    09 February 2017

    DOI: https://doi.org/10.1007/978-3-319-06540-3_24-1

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