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Constraints of Dynamic Carrier Lifetime Techniques

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Quantitative Recombination and Transport Properties in Silicon from Dynamic Luminescence

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Abstract

Dynamic carrier lifetime techniques feature inherent advantages over steady-state techniques. Many of these advantages are related to the immediate access to time domain, which allows a straightforward interpretation without models and a priori assumptions. However, a decay time measurement is not necessarily a carrier lifetime measurement, and caution is required in cases of locally confined (nonuniform) excess carrier generation and recombination. This chapter details key constraints and limitations of dynamic, and particularly harmonically modulated, carrier lifetime techniques—elaborated in the course of this work.

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Notes

  1. 1.

    For nonuniform excess carrier recombination and quasi-steady-state operation conditions, no distinction between harmonically modulated lifetime \(\tau _{eff,h}\) as derived from phase analyses and self-consistent lifetime \(\tau _{\sigma }\) is needed, as these expressions coincide here (cf. Sect. 5.2). Note that this does not hold for injection-dependent recombination properties (cf. Sect. 6.2).

  2. 2.

    The account given in this section is adapted from the corresponding original publication [2].

  3. 3.

    e.g. thick substrates with both, high surface recombination velocity and bulk lifetime, cf. Sect. 8.4

  4. 4.

    This is the case, if a rigorous quasi-steady-state condition is satisfied.

  5. 5.

    Note that \(||y_n ||^2\) has the dimension of a length, thereby rendering \(\beta _n\) dimensionless.

  6. 6.

    For non-negligible transmission through the substrate bulk, cumulative excess carrier density would be reduced by the same factor as cumulative generation rate. Also note that Eq. 6.8 neglects internal reflection of irradiation light, which is however irrelevant if \(\alpha _{\gamma }d\gg 1\).

  7. 7.

    The impact of the injection dependence of recombination properties on harmonically modulated lifetime measurements and other light-biased decay time measurements is thoroughly elaborated in Sect. 6.2.

  8. 8.

    The account given in this section is adapted from the corresponding original publications [6, 7].

  9. 9.

    Aberle et al. previously pointed out that their derivation for surface recombination velocities was transferrable to bulk recombination [9]. The same applies to effective lifetime, being representative of the sum of bulk and surface recombination rates— as already addressed by both Schuurmans et al. [10] and by Schmidt [11].

  10. 10.

    \(\tau _m\left( t\rightarrow 0\right) \) shall be denoted as \(\tau _m\) for reasons of simplicity.

  11. 11.

    For infinitesimal \(G_1\), Eq. 6.32 would be exact.

  12. 12.

    Note that the constant bias generation rate \(G_0\) does not give rise to the mismatch between \(\tau _m\) and \(\tau _{eff,0}\), here. It solely enables the use of the linearized Eq. 6.32 at a finite generation rate.

  13. 13.

    The exact algorithm of the determination of injection-dependent time shifts from harmonically modulated measurements is detailed in Sect. 8.1.2 and in [22].

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

    Johannes Giesecke

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Giesecke, J. (2014). Constraints of Dynamic Carrier Lifetime Techniques. 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_6

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