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In this paper they calculated radiative recombination rates for Germanium using an effective mass model and I am trying to calculate the indirect spontaneous radiative recombination rate related to phonon-assisted transitions from the L-valley to one of the valence bands using eq. (14) (results plotted in Fig. 3). My problem is that for energies $\omega$ large enough, the term in the denominator in eq. (14) independent of $k_{\perp}$ hits zero (since the upper integration boundary of the $\epsilon^{L_c}$ integration scales with $\omega$, just as in eq. (13)). This happens for energies above the band gap, which should be the case for the energy range in Fig. 3. Then the $k_{\perp}$ integral basically is $1/(k_{\perp}^2)^2$ from 0 to $k_{ab/em}^{R_{ind}}$, which diverges.

In the paper I did not see anything mentioned about how they dealt with this problem. Am I doing something wrong, or is there some common way of dealing with an integral like this, so they did not need to mention it in the paper? Would be grateful for any ideas!

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  • $\begingroup$ +1 and welcome to our new community! Thank you very much for contributing your question here and we hope to see much more of you in the future! $\endgroup$ Commented Jan 26 at 22:07

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