Band- or Hopping Conductivity

Whether in a molecular crystal in fact band conductivity or hopping conductivity predominates must be tested using a few simply-defined and physically clear-cut criteria if the mean scattering time x (cf Sect 8.2) is not long in comparison to hjW, where W is the bandwidth, then no discrete value k of the wavevector can be attributed to the charge carriers and a description in terms of an energy-band 

A typical bandwidth of the charge-carrier bands VB and CB in the polyacene crystals is of the order of 0.1-0.5 eV (see Sect. 8.5.4), i.e. r 10 s must hold if one wants to describe the conductivity in terms of a band model. The states of the charge carriers in a band extend coherently over at least several unit cells. Therefore, for a description within a band model, the mean free path X of the charge carriers must be long in comparison to the lattice constant  

Space-charge-limited currents in single crystals will not be treated further here. 

Their existence in ultrapure organic crystals has been verified beyond a doubt (cf for example Fig. 8.27). Particularly in thin crystals such as those used in transistors (see Chap. 12), the currents are space-charge limited for the determination of mobilities, they are however seldom as reliable as TOF experiments using the photoconductivity, due to contact problems between the metal electrodes and the organic crystals. 

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