Consider an indirect-band-gap material such as silicon, with a bias
voltage applied across the material. (For the same of argument, assume
the resulting E-field is in the positive X direction.)
Now let electron-hole pairs (EHP) be generated in the material.
I'm trying to decide where the recombination takes place.
At first, I thought it would (or at least could) take place pretty much
anywhere in the material. (e.g. Say you have an EHP created at x = 1
and another one created at x = 2, where both positions are in the bulk
material and away from contacts. As the holes drift right and the
electrons drift left, the hole created at x = 1 and the electron created
at x = 2 could recombine at x = 1.5, neglecting velocity differences.)
Then I thought about it some more, and realized that the situation is
more complicated than this simple model. (I think.)
The E-field will accelerate the electrons and holes, resulting in a
change in both energy and momentum.
Since the material is an indirect band-gap material, minimums in energy
don't line up with minimums in momentum. So, to meet conservation of
energy and conservation of momentum requirements, a third particle
(phonon or photon) would have to be involved in any interaction (i.e.
recombination).
A three-particle recombination event would seem to be a low-probability
process (e.g. it's hard to impossible to get silicon to lase), so now
I'm thinking that recombination would have to take place in the contact
regions, where the conduction and valence bands overlap, making the
satisfaction of the two conservation requirements much easier.
Am I missing something? Or is this undergrad-level semiconductor device
physics which I've forgotten? If so, can someone provide me with a
pointer?
Bob Pownall
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