Electronic Properties of Solids, lecture 1 (WS15/16)

Conductivity is a valuable parameter to sort materials

conductivity

metals: free e- move through crystall high conductivity → metallic apperance (high reflectance)

other cases: semiconductors, insulators

I = U / R

U = R I (Ohms law)

Band structures

Metal Semi-Metal

Insulator

Semiconductor

Electrons in solids are in bands with finite number density of states- they replace atomic orbitals- we only diccuss electrons that take part in binding

Doped semiconductors

Compensated or poisoned semiconductor (~intrinsic)

both still thermally activated, but level is chosento work at RT ( ca. 50 -100 meV)

InterpretationElectrons in solids are from a physical viewpoint waves in a periodic medium (rather than point chargesin a fluid)→ interference effects→ solids act as heat bath for T>0, collisions

Material properties: band structure

wave vector

Electrons as a wave in free space

Newton:

- quadratic relation because of mass

constant curvature → constant mass high curvature → low mass

Group velocity and the slope of the dispersion Dispersion relation in a periodic media ( t l)

Consequences of the lattice:1) Bragg reflection2) Periodicity of wave function

Filling up the bands: Paulis principle

Example: Na