Can anyone explain to me what a degenerate semiconductor is? How can I recognize when a semiconductor is a degenerate one? Can I find out this from the DOS pattern?
Luis
In terms of the doping, the answer provided above already grasp the point ! Generally speaking, with higher doping into the material, the fermi level (Ef) would move either closer to conduction band (Ec) or valance band (Ev) depending on which type of doping you added, which then gradually become degenerate condition.
While in terms of how to recognize it, one way is that you could calculate it and see if the value is corrected. When we assume non-degenerate condition, we may assume that the energy difference Ec-Ef is greater than 3KT, so that our fermi distribution function could be simplified to exp[-(E-Ef)] or we could call Boltzmann distribution, which help us easily calculate the carrier densities. While if without any assumption and just calculate it, we have to use fermi dirac integral to calculate which is more complex and need to solve by program [Such as : https://nanohub.org/resources/11396] or your could write a matlab code about it.
So the bottom line is that there would be value difference of your carrier densities when using Boltzmann distribution assumption to calculate or not. If you insist to assume non-degenerate condition even Ec-Ef is just 1KT, then the value you calculate may be dramatically different from fermi dirac integral calculation, and it would be wrong to assume non-degenerate condition.
Btw, like Drude formula or Einstein relationship are only valid under non-degenerate condition, so that indeed non-degenerate really help simplify things a lot.
A degenerate semiconductor is a semiconductor with such a high level of doping that the material starts to act more like a metal than as a semiconductor.
look at https://en.wikipedia.org/wiki/Degenerate_semiconductor
In terms of the doping, the answer provided above already grasp the point ! Generally speaking, with higher doping into the material, the fermi level (Ef) would move either closer to conduction band (Ec) or valance band (Ev) depending on which type of doping you added, which then gradually become degenerate condition.
While in terms of how to recognize it, one way is that you could calculate it and see if the value is corrected. When we assume non-degenerate condition, we may assume that the energy difference Ec-Ef is greater than 3KT, so that our fermi distribution function could be simplified to exp[-(E-Ef)] or we could call Boltzmann distribution, which help us easily calculate the carrier densities. While if without any assumption and just calculate it, we have to use fermi dirac integral to calculate which is more complex and need to solve by program [Such as : https://nanohub.org/resources/11396] or your could write a matlab code about it.
So the bottom line is that there would be value difference of your carrier densities when using Boltzmann distribution assumption to calculate or not. If you insist to assume non-degenerate condition even Ec-Ef is just 1KT, then the value you calculate may be dramatically different from fermi dirac integral calculation, and it would be wrong to assume non-degenerate condition.
Btw, like Drude formula or Einstein relationship are only valid under non-degenerate condition, so that indeed non-degenerate really help simplify things a lot.
Hope this will assit
http://www.superstrate.net/pv/physics/degeneracy.html
You may also refer to this link:
https://en.wikipedia.org/wiki/Degenerate_semiconductor
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