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Luminescence of Silicon

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Quantitative Recombination and Transport Properties in Silicon from Dynamic Luminescence

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Abstract

This chapter outlines the theory of spontaneous emission of radiation by non-black bodies such as semiconductors (and particularly indirect semiconductors). The link between electronic properties and luminescent emission is drawn, and elementary approaches to electronic properties from silicon are classified.

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Notes

  1. 1.

    Isotropy of microscopic photon currents accounting for \(n_{\gamma }\) is explicitly not required here.

  2. 2.

    Note that the factor \(m\left( \varepsilon ,\varepsilon _{\gamma }\right) \) is identical for all transition rates of interest, involving the absorption rate, the stimulated emission rate, and the spontaneous emission rate.

  3. 3.

    Note that this expression accounts for isotropic radiation in all directions. Considering radiation only in a solid angle \(\Omega \) would require accounting for the ratio \(\frac{\Omega }{4\pi }\) as another factor on the right side of Eq. 4.15.

  4. 4.

    Some works set \(\mu _{\Gamma }=0\) under the specified conditions [1, 10].

  5. 5.

    This function contains a Bose factor, it carries the energy dependence due to the photon density of states (cf. Appendix A.4), and it contains the absorption coefficient and the inverse squared intrinsic carrier density.

  6. 6.

    Rigorously speaking, the refractive index contained in the velocity of light \(c^{\prime }\) also depends on photon energy \(\varepsilon _{\gamma }\). However, due to a weak energy dependence within the relevant energy range of the silicon luminescence spectrum, it is deemed sufficient to use its average value within this energy range.

  7. 7.

    Here, the effective solid angle of detection also accounts for refraction of light at the interface between a semiconductor and its surroundings, and for light scattering at nonplanar interfaces.

  8. 8.

    Note that this perception of the term intensity differs from the common physical perception of an energy current density.

  9. 9.

    For such photons, the light path in the bulk may substantially exceed its projection on the perpendicular.

  10. 10.

    E.g. the substrate surface corresponding to one pixel of a CCD camera.

  11. 11.

    As indicated in Eq. 4.29, the argument \(z\) of the reabsorption function must be transformed to \(d-z\) for luminescence detection from the substrate interface located at \(z=d\).

  12. 12.

    with derivative phase imaging applications by Melnikov et al. [67] and by Sun et al. [68].

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  1. Fraunhofer Institut für Solare Energiesysteme ISE, Freiburg, Germany

    Johannes Giesecke

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Giesecke, J. (2014). Luminescence of Silicon. In: Quantitative Recombination and Transport Properties in Silicon from Dynamic Luminescence. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-06157-3_4

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