00:01
41 .34, there are these two things we're supposed to show that are true.
00:08
This has to do with if we have an undoped semiconductor, we can have a simplified model where we replace the actual distribution of energy states with just having nv states in the valence band that all have the same energy, and nc states in the conduction band that all have the same energy.
00:37
And given that and if the number of conduction electrons is equal to the number of valence holes, we need to show that this is true.
00:50
And the next part, if we have going from this, if the fermi energy is in the gap and the difference between the fermi energy and the two, the conduction in valence energies is much larger than the thermal energy, we can derive this expression.
01:15
So the number of electrons in the valence band is this nv, so the density of valence states times the occupation probability.
01:56
So ev minus ef over kt plus one.
02:15
Now in the valence band we want the holes.
02:26
So the number of holes in the valence band, since the number of available states has to add up to the number of available states, we can subtract this expression we just found from nv, and we'll end up with this.
03:10
This is one of the things that is supposed to be equal to the other.
03:14
This is delta ev.
03:17
So so far things are looking good...