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Carrier Recombination and Noise

Book cover Semiconductor Physics

Abstract

In steady state, for each act of carrier generation or excitation there must be one inverse process of recombination or relaxation. Carriers can return immediately or after scattering to their original state, or they can recombine radiatively or nonradiatively with another state.

Nonradiative recombination is almost always defect-center controlled; it releases energy in the form of phonons, or in Auger recombination, by accelerating another electron. Phonon emission occurs as a single-phonon process when trapping a carrier at a shallow defect center, or as a multiphonon emission when recombination occurs at a deep center. In carrier traps, which are located close to one band, excitation into the adjacent band and trapping at the center dominate, while in recombination centers, which are located closer to the center of the bandgap, carriers recombine from one band to the other. The capture cross-section of defect centers spread over more than 12 orders of magnitude.

Radiative recombination proceeds as an emission delayed by the lifetime of an excited state and changed in energy after relaxation of the excited state. The spectral distribution of the luminescence is related to the electronic structure of the semiconductor and its defects. The sharp low-temperature spectra of shallow-level defects in pure crystals are well understood, while the assignment of the broad emissions of deep defects with strong lattice coupling is usually difficult.

The random fluctuation of individual carrier motion and carrier generation-recombination creates noise. Equilibrium noise is caused by the Brownian motion of carriers and independent of the frequency. Nonequilibrium noise is generated upon optical excitation or current injection and has usually a typical 1/f frequency dependence. It is composed of various contributions; a fundamental part originates from energy loss by low-frequency bremsstrahlung in basically elastic scattering processes. Noise creates a lower limit for signal detection.

K. W. Böer: deceased

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Notes

  1. 1.

    It is interesting to see that Eq. 24 can be rewritten, using the quasi-hydrogen energy EqH, as

    $$ {\tau}_{\mathrm{A}}\cong \frac{h}{E_{\mathrm{qH}}}\frac{E_{\mathrm{g}}}{k\;T}\exp \left(\frac{E_{\mathrm{g}}}{k\;T}\right). $$
    (25)

    The first part of Eq. 25 represents the Heisenberg uncertainty relation, indicating that τA cannot be smaller than the Heisenberg uncertainty time for an exciton, τA ≥ l.6·10−13 s. This presents a lower limit for Eg ≅ kT for the approximation used.

  2. 2.

    Other radiation due to nonlinear optical processes, such as photon (Raman or Brillouin) scattering and higher harmonic generation, are also excluded in this discussion. These are discussed in Sect. 3.3 of chapter “Photon–Phonon Interaction”.

  3. 3.

    The binding energy of excitons bound to donors or acceptors is proportional to the ionization energy of these defects (Hayne’s rule, Sect. 2.2 of chapter “Shallow-Level Centers”).

  4. 4.

    The term phosphor should not be confused with the chemical element phosphorus, which emits a faint glow when exposed to oxygen. This property is related to its Greek name Φωσφόρος, meaning light bearer, which also lead to the term phosphorescence to describe a glow after illumination, and the general term phosphor for fluorescent materials.

  5. 5.

    In contrast to the vacuum diode, the current in a semiconductor is bidirectional, hence the factor 2.

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  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. (2020). Carrier Recombination and Noise. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_30-3

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    Carrier Recombination and Noise
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_30-4

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    DOI: https://doi.org/10.1007/978-3-319-06540-3_30-3

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    DOI: https://doi.org/10.1007/978-3-319-06540-3_30-2

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    Carrier Recombination and Noise
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_30-1

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