Electron affinity, work function, band gap

[aaaa202]

What exactly is the relation between these 3 quantities?
As far as I can tell the work function is the energy needed to bring an electron from the fermi level out into vacuum, while affinity is from the bottom of the conduction band.
Does this then mean that they can be used to calculate the band gap between the conduction band and valence band? For me it would appear so since you normally say that the fermi level is midway between the valence and conduction band. But is this always true, and why is it true?

 

[ZapperZ]

What exactly is the relation between these 3 quantities?
As far as I can tell the work function is the energy needed to bring an electron from the fermi level out into vacuum, while affinity is from the bottom of the conduction band.
Does this then mean that they can be used to calculate the band gap between the conduction band and valence band? For me it would appear so since you normally say that the fermi level is midway between the valence and conduction band. But is this always true, and why is it true?

It's easier if I show you a sketch, so I took a couple of pages from one of my presentations:

Note that only for the metal is the "work function" equals to the photoemission threshold. This is because the work function, defined as the energy between the Fermi level and the vacuum level, sits in the middle of the gap for an intrinsic semiconductor. There are no states there! So instead, the photoemission threashold is the energy from the top of the valence band (which is filled) to the vacuum level.

So no, you can't use the work function minus the electron affinity to find the band gap. Rather, you have to use the photoemission threshold minus the electron affinity.

Zz.

 

[aaaa202]

but what about the affinity minus the work function times 2? Shouldn't that give the band gap?

 

[ZapperZ]

but what about the affinity minus the work function times 2? Shouldn't that give the band gap?

Of course you can, but is there a reason that you are fixated with using the electron affinity?

But be careful. This ONLY works for an intrinsic semiconductor when you make the assumption that the Fermi level is right in the middle of the gap. This is no longer true for extrinsic semiconductor, so in this latter case, you can no longer use that deduction.

Secondly, the electron affinity for a semiconductor requires a bit more "work" to get, especially from experiments, unlike, say, atoms. One can get the band gap value more directly (and easier) than the electron affinity. The same can be said about the photoemission threshold. So more often than not, those two values are used to arrive at the electron affinity in a semiconductor, rather than the other way around.

Zz.