Band versus Hopping Conduction

The differentiation between whether delocalized (band theory) conductivity or diffusionlike hopping conductivity best explains experimental conductivity results is not always easy in practice but can be made by a comparison of the theoretical expressions for electrical conductivity and mobility of the charge carriers in a solid. 

For a metal that obeys band theory well, and conducts by electrons, the conductivity can be written  

For a metal, therefore, cr decreases with temperature, thus  

In the case of elemental semiconductors such as Si, which are also well described in band theory terms, the equation for the conductivity is composed of an electron and hole component so that  

TABLE 7.1 Electrical Conductivity and Mobility of Charge Carriers in Metals, Band-like Semiconductors, and Hopping Semiconductors 

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