In a crystalline solid each atomic level 'splits' into n levels (n = number of atoms in the system). When the number of atoms is large each level becomes replaced by a band of closely spaced levels.
In a semi-conductor we have an empty "conduction band" and a fully occupied "valance band". Conductivity arises because electrons get excited to the conduction band.
Question: Why can't electron in the valence band freely move around and therefore conduct electricity? My question also applies to metals where the conduction band is already half-filled. What's special about this conduction band that allows electron to move around freely?
Answer
Every energy level in a band has an associated momentum, and the total momentum of all the levels in a band is zero. Because the total momentum is zero there can be no net movement of electrons and hence no current. In effect, for every electron with momentum $p$ there is another electron with momentum $-p$ and they cancel each other out.
You can't change the momentum of any of the electrons in a filled band by applying an external field because all the energy levels are full. There are no empty levels for you to move your electron into. That means an external field cannot cause a net movement of electrons.
When you excite an electron into the conduction band it will go into a low momentum state, but there are available states above it with higher momenta. Apply an external field and you will move the electron up into a state with higher momentum that is lined up with the field. In this state the electron has a velocity aligned with the field so there is a net movement of electrons and therefore a current.
The same effect causes a current in metals. There are empty states for the electrons in the band to move into.
No comments:
Post a Comment