SCEN103 Class 23

Introduction to Electronic Band Structure

• Pauli exclusion principle still holds!
• Electrons on neighboring atoms "overlap" and must shift energies slightly to that each stays out of the others' states.
  ---- more detailed quantum physics
• Energy levels "blur" into energy bands.

Conductor or Insulator?

• Depends on separation of bands and
  whether band is full or not.
• With N atoms making up the solid,
  each band may hold 2N electrons.
  ---- related to filling of electronic orbitals
• Consider example of following two elements, referring to our abridged Periodic Table
  

  Name	# electrons	Configuration
  neon:	10	1s2, 2s2, 2p6
  sodium:	11	1s2, 2s2, 2p6 3s1
  		or [neon] 3s1

• Since the number of electrons in sodium is odd, the last band up is only half-filled. The even number of electrons in neon fills the final band.

So how does this help explain why sodium is metallic and solid neon is an insulator?

• To have an electrical current in a solid, conduction electrons must be able to move through the solid by addition of some energy from an applied voltage.
• The energy level of conduction electrons can be approximated by the thermal energy, 0.025 eV at room temperature, smaller for lower temperature.
• The relative separation of bands must be considered;
  How far away is the next unfilled band?
• Remember that electrons are not permitted in the forbidden bands
• In neon,
  • The energy separation between the nearest empty band and the closest filled band is around 20 eV.
  • For conduction to take place in neon, the electrons in the upper most band, completely filled, would have to "jump" across the band gap of 20 eV, very unlikely with only 25 meV of energy kT!
• In sodium,
  • The band is partially filled, thus a "little bit" of energy can be added to the electrons -- no quantum jump is involved.
  • The final electrons "added" to make sodium, the 3s1 electrons, are very easy to strip from the "neon" ion core. They become the conduction electrons, often known as the free electrons in the metal.
• Note the orbital configuration of the following elements that happen to be excellent conductors as solids:

  Name	# electrons	Configuration
  aluminum:	13	[neon], 3s2, 3p1
  copper:	29	[argon], 3d10, 4s1
  silver:	47	[krypton], 4d10, 5s1
  gold:	79	[xenon], 4f14, 5d10, 6s1

• This is not to say that all conductors have one electron in an unfilled band -- but the best conductors do!

My article on Insulators written for encyclopedia