Electronic Properties of Crystals

1. e.g. Li+ Electronic Properties of Crystals Metallic State e- SEA OF MOBILE VALENCE ELECTRONS ? Metals are good electric and thermal conductors: - good in comparison with what -microscopic description allowing for quantitative predictions ?

2. Def. of electrical resistance: Independent from geometry of the sample current Voltage drop This is not Ohm´s law Ohm´s law: =constant independent from V ? Metals follow Ohm´s law why Drude model Material specific quantity:

3. Alternative formulation of Ohm’s law with the help of V E L The inverse resistivity is called conductivity more general in the non isotropic case A Voltage drop V=E L Current density: I A A

4. Covers 25 orders of magnitude

5. Drude model First simple classical model for a free electron gas friction due to the scattering processes Classical equation of motion: electric force F=qE accelerating the charge q=-e0 where vD is the drift velocity superimposed to the random thermal velocity

6. relaxation time dQ=q dN where Switching off the electric field Relaxation to the thermal velocity within Stationary state in an electric field: 0 dV=Adx

7. consistent with Ohm’s law preserved in quantized models effective mass However, parameters like, e.g., the electron mass become modified Classical description fails completely in explaining the heat capacity of electrons Classical: N Electrons not observed in experiment