Why is it that at the wavelength corresponding to the bandgap of an indirect semiconductor, the internal quantum efficiency doesn't drop immediately to zero? But instead, it follows a sharp curve to zero that extends till beyond the bandgap wavelength.
The carrier can be influenced by quantum fluctuations, adding some small amount of energy to to the carrier in the higher state and than making it possible to recombine. This effect is also known from direct semiconductors but there you have got a smoother exponential drop. The difference in drop behaviour from first (indirect) to second (direct) is that the first is taking into account three effects:
1. carrier has to be influenced by a photon
2. carrier has to be influenced by quantum fluctuation (to get over the band gap)
3. carrier has to be influenced by a phonon to get back on the band
Since the second action is very unlikely, you will get a very fast drop which is still exponential but it looks linear because it is so fast ...
I would like to add a comment to clarify the third point. Quantum efficiency can be non-zero below the bandgap because of phonon-scattering. Photon absorption in an indirect bandgap semiconductor enables a charge carrier (electron) transition from the top of the valence band into a virtual state, from where it scatters into the conduction band by phonon interaction. In the case of phonon absorption, the virtual state energy level can lie below the bandgap energy.
Then, excitons can play a role, as well. A bound electron-hole-pair can be created by an energy that is smaller than the sum of energies of a free electron and hole.
Finally, impurities often cause shallow levels (just below the conduction band), giving rise to below-bandgap absorption.
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