Electrical Conductivity Measured Data Material s 1Wm Copper

Electrical Conductivity Measured Data Material s [1/(Wm)] Copper, Silver Iron Manganese Germanium Silicon Gallium arsenide (Ga. As) Glass Porcelain Rock salt (Na. Cl) Silica 5× 107 1× 107 2× 105 1× 100 1× 10 -3 1× 10 -6 1× 10 -9 1× 10 -13 1× 10 -15 2× 10 -18 1025 1

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

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) 3

Effect of the crystal structure Graphite Diamond 4

Electrical Conductivity Classical Drude’s Theory … equation of motion … maximum drift velocity … solution of the equation of motion - … time between two collisions … Fermi velocity 5

Electrical Conductivity Classical Drude’s Theory Microstructure defects acting as scattering centers for electrons: Ø Point defects (foreign atoms) Ø Line defects (dislocations) Ø Planar defects (crystallite and grains boundaries, stacking faults) Ø Volume defects (precipitates) 6

Electrical Conductivity Quantum Mechanical Theory Fermi surface (a) without and (b) with an electric field 7

Electrical Conductivity Classical Theory Ø Ø All electrons* are in motion and contribute to the electrical conductivity Change of electron density in electric field * valence electrons 8

Quantum Mechanical Theory of Electrical Conductivity N(E) … density of states NF … number of electrons at the Fermi level Drude: 9

Quantum Mechanical Theory of Electrical Conductivity Two-dimensional Fermi surface Three-dimensional Fermi surface 10

Density of States and Number of Electrons per Volume 11