We know that the electron states in an isolated atom (1s, 2s, 2p, etc) however what happens to these electron states when we bring isolated atoms together to form solids?
5.2 Core Levels
Figure 5.1 - A Atomic Potential Well
If we consider a lone atom its electronic states are bound tightly to the atom, this is over a radius of about 0.5nm . To remove an electron from the lower levels a lot of energy is required so as a solid they essentially do nothing in relation to the properties of a given material. For this reason this will not really be consided in relation to Solid State Physics.
5.3 Electron Bands
We consider two atoms which are far apart can be modelled as a finite square well potential.
Figure 5.2 - Two Atoms Far Apart
if X is very large then the wavefunctions tend to behave as if they where functions of isolated atoms. However as X decreases the higher energy states touch first interacting quantum mechanically. For example state |1> (normally the higher states touch first)
Figure 5.3 - Higher States Touching First
the states hybridise into Bonding and Anti-Bonding states. The bonding state in hydrogen has a minimum amount of energy which can accomadate two electrons which their spin in opposite directions.
Figure 5.4 - Minimum Bonding Energy State
However if we consider six atoms that has been seperated by a distance X where we now have to consider electronic states have higher orbital states.
Figure 5.5 - Six Atoms Being Brought Together
if the number of electrons present per atom were enough to exactly fill all the levels which started at |3> the lowest energy might be at X0 . We note however that each band contains one electron state for each original atom (or lattice point in a crystal).
5.4 Bands in Molecules
If c=ct is a tiny for a one dimensional solid then the bonding/anti-bonding energy seperation is about 7.7eVl-1 which is about 160nm . If we put a chain of carbon atoms together be get
Figure 5.6 - Carbon Bonding/Anti-Bonding Energy Levels
However the bands in solids are in the order of about 1019 different energy states (for example in a salt grain). From the bands of state the transistions happen between bands, not within them, for example in opto-electronics.
