1. 1 Electrical Conductivity Measured Data Material  [1/(  m)] Copper, Silver 5×10 7 Iron 1×10 7 Manganese 2×10 5 Germanium 1×10 0 Silicon 1×10 -3 Gallium arsenide (GaAs) 1×10 -6 Glass 1×10 -9 Porcelain 1×10 -13 Rock salt (NaCl) 1×10 -15 Silica 2×10 -18 10 25

2. 2 Basic Equations … Ohm’s law … current density, electric field … electrical resistance, electrical resistivity

3. 3 Electrical Conductivity – Drude’s Model electron gas * in the material Number of atoms/electrons in alkali metals per m 3 Free electrons … Interaction with crystal lattice … * valence electrons are assumed to be completely detached from their ions (free electron theory)

4. Effect of the crystal structure 4 Graphite Diamond

5. 5 Electrical Conductivity Classical Theory … equation of motion … maximum drift velocity … solution of the equation of motion … time between two collisions … Fermi velocity

6. 6 Electrical Conductivity Quantum Mechanical Theory Fermi surface (a) without and (b) with an electric field

7. 7 Electrical Conductivity Classical Theory  All electrons * are in motion and contribute to the electrical conductivity Change of number density in an electric field * valence electrons

8. 8 Quantum Mechanical Theory of Electrical Conductivity

9. 9 Two-dimensional Fermi surface Three-dimensional Fermi surface

10. 10 Density of States and Number Density