electron band structure?

Question

we know that there is a valence band, forbidden band and a conduction band of electrons for an atom. For conduction to take place electrons in the valence band need to gain energy and jump to the conduction band.

but say for pure silicon can an electron exist in the forbidden band?
how about for doped silicon?

Answer 1

Here's the key you need to keep in mind: these bands don't exist in a single atom. They are formed from combinations of orbitals from neighboring atoms. Now, if every atom had exactly the same relationship with every neighbor with which it could interact, there wouldn't be 'bands' at all... they'd be LINES. But because there are slight irregularities (the same thing that causes electrical resistance) you get a band - the electron can go in one direction with one amount of energy and in a slightly different direction with a slightly different about of energy. It doesn't LOOK quantized, but really it still is.

What the forbidden bands are, then, are areas where none of the sums add up at all. No matter how you add the numbers 9, 10, and 11, you will never get a sum of 15. It is forbidden. And that means that under normal conditions there is simply no way that an electron is going there.

The only way those conditions are going to change is if you change the positions of the bands themselves, either through an outside force or through using different materials. If you're adding 7, 8, and 9, then suddenly 15 isn't so forbidden any more. But at that point it's more like you're looking at a completely different problem than that you're putting something in a forbidden band - under those circumstances that's not forbidden at all, and its new forbidden bands are just as forbidden.

Short version: If an electron could hang out in the forbidden band, it wouldn't be forbidden now, would it?