Electrical Conductivity Measured Data Material Copper Silver Iron
- Slides: 13
Electrical Conductivity Measured Data Material Copper, Silver Iron Manganese Germanium Silicon Gallium arsenide (Ga. As) Glass Porcelain Rock salt (Na. Cl) Silica [1/(Wm)] 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 V … electric field A … current density … electrical conductivity, resistance, specific resistivity 2
Basic Equations Current density S Ohm’s law Electrical conductivity 3
Electrical Conductivity – Drude’s Model Free electrons in materials Number of atoms/electrons in alkali metals per m 3 Free electrons … Interaction with crystal lattice … 4
Effect of the crystal structure Graphite = 2 to 3× 105 S/m // basal plane = 3. 3× 102 S/m ⊥ basal plane Diamond ~ 10− 13 S/m 5
Electrical Conductivity Classical Drude’s Theory … equation of motion … maximum drift velocity … solution of the equation of motion … time between two collisions - … Fermi velocity 6
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) 7
Effect of the Number of Free Electrons on the Electrical Conductivity in Metals The larger the number of electrons and the higher the Fermi energy, the higher is the electrical conductivity. The temperature and the effect of the Fermi function on the 8 number of free electrons play a minor role.
Electrical Conductivity Quantum Mechanical Theory Fermi surface (a) without and (b) with an electric field 9
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 10
Quantum Mechanical Theory of Electrical Conductivity Drude: N(E) … population density of electrons NF … number of electrons at the Fermi level 11
Quantum Mechanical Theory of Electrical Conductivity Two-dimensional Fermi surface Three-dimensional Fermi surface 12
Density of States and Number of Electrons per Volume 13