Solid State Physics

NPFD

Greetings all this is my first post in this forum. I've got a Solid state physics homework question (i know that the intent of this forum is not to do homework, all i want is guidence in the correct direction not the answer itself.) Any way here it is:

A conduction band electron in silicon is in the (100) valley and has a k-vector of 2pi/a (1.0, 0.1, 0.1). Calculate the energy of the electron measured from the conduction band edge. Here 'a' is the lattice constant of silicon (5.43 Å).

Any ideas on where to begin?

arcnets

Welcome NPFD,
even though you seem to have nothing so far, I think it's OK if I give the following hint:

If you know the k vector, then you also know the momentum vector. Now, how is kinetic energy linked to momentum?

NPFD

Thanks for the reply. I guess my question was a little vague, sorry for the confusion. I understand what you are saying with relating momentum and energy but i guess what i am unclear on is that i should calculate the energy from the "conduction band edge." How is this different from finding the energy anywhere else in the band? Are they simply asking find the maximum energy an electron can hold before it jumps to the next level?
For the sake of clearity let me show you what i have so far. I've got a k-vector of 2pi/a (1.0, 0.1, 0.1), where a=5.43. So my vector is:
k-vector=(0.368, 0.0368, 0.0368)

I also know that:
E(k-vector)=((hbar^2)(|k|^2)/2m.

After doing this i found the energy to be E(k-vector) = 0.033. So as i was saying how is this energy different from that of the energy at the "conduction band edge?"

arcnets

Looks OK to me, but your answer should have a unit. I think the standard unit in a problem like this should be electronvolts.

What is meant by 'conduction band edge'? I'm not sure, but I guess, to be in the conduction band, an electron must have some average linear momentum, i.e., must not be bound to a single nucleus. Thus, I guess what they ask for is just the kinetic energy as calculated from the linear momentum. As you did.

salsero

"Calculate the energy of the electron measured from the conduction band edge."

Energy is defined up to an additive constant. The instruction above means that the energy of the conduction band edge should be considered as zero.
[:)]