Semiconductor Holes and Excitons

Most recent answer: 09/20/2013

Q:
Why is an electron hole in a semiconductor represented as a flipped or inverted particle-in-a-box? Also can you explain excitons?
- Dylan (age 20)
Ithaca, NY, US
A:

I'm not sure what you mean by the first question, but perhaps it will help to borrow a standard picture of the band structure and explain it.


These pictures show what the energy is for different electron states as a function of the electron "wavevector"- a measure of how much the phase of the wave function changes as you go from one crystal cell to the next. The different bands come from different structures of the wavefunction within each cell. At low temperature in an undoped semiconductor, all the lower band states are filled and all the upper ones are empty. If an electron picks up enough thermal energy to jump up into the upper (conduction) band, it leaves an empty state (hole) in the lower (valence) band.  The part that you may be asking about is why the valence states we're interested in have decreasing energy as the wavevector differs from some special value (sometimes zero). The reason is that the first states likely to lose electrons are the highest energy ones, at the top of the band.

On excitons, I strongly recommend this clear little Wikipedia article: . Notice the beautiful illustration from our colleague Peter Abbamonte.

Mike W.


(published on 09/20/2013)