Fermi Energy Matching in Semiconductors

[tiddwaylll]

I have taken several courses in semiconductors at the undergraduate level. Both the pure physics part (k vectors) and the more engineering parts (silicon processing, band diagrams) etc.

So for all the junctions (Schottky, Ohmic, p-n) - I have never managed to imagine the idea of the Fermi level in clear terms.

So we have the valence band, which I understand is where all the sea of valence electrons are stored. In some sense they are fixed there with their respective parent atoms. Then there's the conduction band where all electrons that can "move" within the solid stay. Valence band electrons given a quantized amount of energy can jump the band gap into the conduction band.

So what does the fermi energy mean? From googling, I find that at 0K, the sea of electrons will be at the fermi level. Does this mean the valence band "rises" up to the fermi level? At temperatures greater than 0K, there is a finite probability of electrons being "higher" than the fermi level. So does this mean that electrons stay at a some probability between the valence band and the fermi level and at another probability jump into the conduction band?

Lastly, the most baffling thing is how many textbooks just shrug off junction contact as "the fermi levels need to match up - thus the valence and conduction bands bend."

WHY does the fermi levels need to match up? What does it mean physically when the two fermi levels in a solid are "matched" ? I tried to do this with the analogy of two water tanks above and below each other but couldn't get any fermi levels into the analogy.

Btw, I understand most of the basics of semiconductors - the electrons and holes diffusing etc etc - and can calculate the numbers without understanding the above. But I would really like to know. Thanks for any help given!

 

[nickjer]

The sea of electrons analogy is probably talking about metals where there is no clear definition of a valence and conduction band. So at 0K, the electrons fill up all the energy levels up to the Fermi level.

For semiconductors there is no clear Fermi level. Some put it at the top of the valence band and others (in terms of doping) set it at the midpoint in the gap. You can find equations online where they choose the Fermi level at the midway point in the gap when you have no doping, and how it changes with doping concentration.

Matching the Fermi level... That comes from statistical mechanics. When you bring two systems together the chemical potential (i.e., Fermi level) for both needs to be the same for the system to be in equilibrium. So the free charges will rearrange themselves to satisfy this equilibrium, leading to band bending.