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Semiconductor Physics pp 1–36Cite as

Carrier Transport in Low-Dimensional Semiconductors

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Abstract

Carrier transport in semiconductors with reduced dimensions is determined by the low-dimensional density of states. In two-dimensional systems such as quantum wells and superlattices, the carrier mobility is highly anisotropic. Parallel to the barriers it may exceed the bulk value by far in a two-dimensional electron gas at low temperature. Perpendicular to the interfaces, carriers have to penetrate the barriers and the mobility is low. Tunneling through thin barriers is an important process; it is enhanced when matched with quantized energy levels and leads to negative differential resistance. In one-dimensional quantum wires, ballistic transport occurs and the conductance gets quantized. Transport through a zero-dimensional quantum dot is affected by charging with single electrons, giving rise to a Coulomb blockade with zero conduction at certain bias values.

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Notes

  1. 1.

    The analogous system with holes as free carriers is called two-dimensional hole gas (2DHG) . Due to their smaller effective mass usually electrons are preferred as carriers in transport devices.

  2. 2.

    Such a device is also referred to as high-electron-mobility transistor (HEMT) or two-dimensional electron gas field-effect transitor (TEGFET). Typical Al mole fraction x of Al x Ga1-x As and donor-doping level are 0.30 cm−3 and 1018 cm−3, respectively. Donor doping stops at a spacer distance d (typically on the order of 10 nm, see Fig. 5) away from the interface to GaAs.

  3. 3.

    For resonant tunneling of holes, see, e.g., Hayden et al. (1991).

  4. 4.

    Heavy holes in the valence band get localized much stronger due to their larger effective mass.

  5. 5.

    A nonthermal electron distribution in the active region makes laser action possible even in the absence of a global population inversion, see Faist et al. (1996).

  6. 6.

    The transfer from E 2 to E 1 gets particularly efficient if their difference equals the energy of an LO phonon, thereby inducing resonant electron-LO-phonon scattering.

  7. 7.

    The current is usually measured by applying a slow continuous sweep of the bias. As the branches overlap, different parts of the branches are observed for sweep-up and sweep-down.

  8. 8.

    We focus again on electron gases; one-dimensional transport structures made using 2DHGs (two-dimensional hole gases) were studied as well, see, e.g., Danneau et al. (2006).

  9. 9.

    In the classical description the phase correlation of the carrier wavefunctions before and after scattering are destroyed. In the description of quantum diffusion the phase correlation is limited by inelastic scattering events only; the corresponding mean scattering time τ ϕ is at low temperatures significantly larger than τ.

  10. 10.

    The conduction step 2e 2/h corresponds to a resistance of 12907 Ω.

  11. 11.

    The degeneracy may already be lifted at zero magnetic field if there is a spontaneous spin polarization due to electron interactions (Chen et al. 2008), see the section on the “0.7 conduction anomaly” below.

  12. 12.

    Instead of a factor T also a factor T/(1−T) = T/R is found in literature. The difference arises from the location where V 1,2 is measured. In a two-terminal measurement with I and V measured through the same pair of leads a factor T results, while an ideal (noninvasive) four-terminal measurement yields a factor T/R; for a small T of the conductor both measurements coincide; for details see Engquist and Anderson (1981).

  13. 13.

    This requirement for R tunnel is related to Heisenberg’s uncertainty relation: quantum fluctuations in the number of electrons on the dot due to tunneling through the barriers must be much less than one for the duration of measurement. In addition, the charging energy must exceed the thermal energy (see text). The characteristic discharging time of the dot is then Δτ = R tunnel C dot, and the uncertainty relation yields ΔEΔτ = (e 2/C dot) R tunnel C dot > h, or R tunnel > h/e 2.

  14. 14.

    If the considered disk is replaced by a sphere, the factor 8 in the capacitance formula is replaced by a factor 4π. The simple consideration in the text does neither include single-particle energies of a dot with charge Ne nor external charges or capacities (e.g., from a gate electrode).

  15. 15.

    The level spacing is given by the scaling ħ 2 π 2/(m n L 2) times a factor, which depends on the dimensionality of the “dot” (Kouwenhoven and McEuen 1999); L is the size of the confining box. In 1D, 2D, and 3D the factors are given by N/4, 1/π, and 1/(3 π2 N), respectively. The spacing in lateral dots (2D) does not depend on the number of confined electrons N.

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  1. 138 Moorings Park Rd. O 301, Naples, FL, USA

    Karl W. Böer

  2. Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstr. 36, Berlin, 10623, Germany

    Udo W. Pohl

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Böer, K.W., Pohl, U.W. (2017). Carrier Transport in Low-Dimensional Semiconductors. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_27-1

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    Carrier Transport in Low-Dimensional Semiconductors
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_27-4

  2. Carrier Transport in Low-Dimensional Semiconductors
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_27-3

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    DOI: https://doi.org/10.1007/978-3-319-06540-3_27-2

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    Carrier Transport in Low-Dimensional Semiconductors
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_27-1

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