Lecture 18: Semiconductors and Superconductors

There is information on 2 web sites and in your textbook that will help you understand this field.
  1. There is an excellent web site on the properties of semiconductors by a group at the University of Glasgow.
  2. Textbook: section 5.9
  3. Superconductors.Org has a simple and easy to understand page on the basics of superconductors.
  4. Textbook: section 27.4
After reading this material, go to WebCT and take a quiz.

Conductors and Insulators

In any solid, metallic (such as Zn), ionic (such as NaCl), or covalent (such as SiO2), the valence orbitals of atoms and molecules combine to form molecular orbitals. The number of molecular orbitals is equal to the number of atomic orbitals, and for any material, this is a very large number but the energy difference between highest and lowest doesn't change by much. Many orbitals separated by very small energy gaps give rise to bands of orbitals.



For sodium metal, the band is made up of molecular orbitals formed from the combination of 2s atomic orbitals and about half of the orbitals are filled. There is only a very small energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). When an electron goes to an unoccupied orbital with available thermal energy, it is free to travel throughout the metal. The "hole" left in the HOMO can travel too.

In silica (SiO2) there are covalent bonds between each silicon and 4 oxygens around it that are combinations of Si 3s and 3p atomic orbitals and O 2s and 2p atomic orbitals. We can think of the molecular orbitals forming similar bands but there is a large energy separation or band gap between the occupied and unoccupied levels. The electrons in the orbitals of silica are not free to travel and the material is an insulator.



In pure, crystalline silicon, there is also a band gap between the occupied and unoccupied molecular orbitals but it is smaller. Electrons in the filled valence band can be promoted to the conduction band by thermal energy or when the material aborbs light. The electrons would then be free to travel through the material and holes (electron vacancies) would travel through the valence band.



Key Points on Semiconductors

Silicon and germanium are intrinic semiconductor that have semiconducting properties as pure materials. These elements have the same crystalline form as diamond, an insulator, but their lattice constant,a (width of the cube) is much larger. These elements each have 4 valence electrons.

What about mixtures? A mixture of 50% Ga and 50% As would also have an average of 4 valence electrons and this substance forms crystal that have the diamond lattice, just like Ge. The material gallium aresinde is also a semiconductor. Can you think of others?



Adding a very small amount of certain materials to a host material can transform it into a doped semiconductor. If the dopant has more valence electrons than the bulk, the resulting semiconductor is a n-type. For example, a crystal of Si with a few atoms of P is an n-type semiconductor. A dopant with fewer electrons than the bulk material gives a p-type semiconductor. You can make this kind of semiconductor by adding a few atoms of Al.

Key Points on Superconductors

The conductivity of metals and of semiconductors changes with temperature. Why? It's because the electrons flowing through a material will always pass close by positively charged nuclei. This impedes flow. As temperature increases, there is more thermal motion of the nuclei and this resistence increases. Resistivity is a property of the metal or semiconductor.



In superconductors, the resistivity goes to zero at some temperature. In these materials, electrons travel in pairs with opposite spin. When one electron of a Cooper pair goes past a positive charge in the lattice, lattice vibrations accellerate the second electron. The weakly bonded pairs are not impeded by lattice cations in the same way as single electrons.



Some of the recently discovered high temperature superconductors are based on Perovskites. You drew the lattice of CaTiO3 last week and most of you drew a cubic lattice of Ca with Ti in the cubic hole and oxygen atoms on the edges. Another perovskite with the same structure is BaCuO3 You could also draw the same lattice as a cubic array of copper atoms. Now imagine that some of the oxygen atoms have been removed and 1/3 of the barium atoms have been exchanged for yttrium. You would have the basic structure of a 1-2-3 material or YBa2Cu3O7.



Superconductors have another interesting property. They are perfect diamagnets exclude magnetic fields.