Delocalized band model

Observations with microcrystals of semiconductor sihcon have shown that the transition from the model of localized electron levels quantum size) to the band model of delocalized electron levels (microscopic or macroscopic size) occurs at about 2 nm [Kanemitsu-Uto-Masumoto, 1993]. It appears, then, that the band model can apply to passive films thicker than 2 nm. Further, accoimting that the film interacts with the substrate metal, the band model may apply even to the range of thickness less than 2 nm. 

Many ferromagnets are metals or metallic alloys with delocalized bands and require specialized models that explain the spontaneous magnetization below Tc or the paramagnetic susceptibility for T > Tc. The Stoner-Wohlfarth model,6 for example, explains these observed magnetic parameters of d metals as by a formation of excess spin density as a function of energy reduction due to electron spin correlation and dependent on the density of states at the Fermi level. However, a unified model that combines explanations for both electron spin correlations and electron transport properties as predicted by band theory is still lacking today. 

The simplest model of charge transport in delocalized bands is the Drude model, which assumes the carriers are free to move under the inhuence of an applied electric held, but subject to collisional damping forces. Note that the scattering centers are not the nuclei of the background material, but rather phonons (lattice vibrahons) or impurities. A statistical equahon for estimahng the mean drift velocity of the carriers in the direction of the electric held may be written as... 

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