Semiconductivity in perovskites

Many perovskites in the insulating state are, in fact, semiconductors. There are several models for the mechanism of charge transport, which can generally be differentiated by considering the temperature variation of the conductivity or resistivity of the sample. If the conductivity can be considered to be due to itinerant electrons promoted to an empty conduction band by thermal energy and holes left 

This form of the resistivity is often found at higher temperatures. If the value of Tq is small so that the exponential term can be expanded to give the 

If it is assumed that a migrating electron suffers a Coulombic attraction with the hole remaining on the parent cation, then the Efros-Shklovskii variable-range hopping law is appropriate  

It is found that the Mott variable-range hopping law often holds at intermediate temperatures and the Efros-Shklovskii variable-range hopping law at lower temperatures. 

In many perovskites, the distortion may be considerable, as with the Jahn-Teller effect or the influence of lone pair electrons. In such cases the distortion may prevent any charge carrier migration at all, and semiconducting behaviour is suppressed. Changing the degree of distortion by substitution will often reverse this. 

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