Well, actually they are NOT exponential, but exponential square or gaussian. At first glance this may seem a slight or neglectable difference but actually is just the opposite. This difference is constitutive and very critical, since it enables the existence of a transport level, and explains many features of carrier transport by hoping in disordered materials . For more information, refer to "Charge Transport in Disordered Organic Materials" by Sergei Baranovski. Cheers.

The density of states in valence and conduction band are depending exponentionly with energy and the statistical distribution also depending exponentionly .

This is normally called an Urbach tail- see for example http://gradworks.umi.com/33/53/3353549.html

This is normally called an Urbach tail- see for example http://gradworks.umi.com/33/53/3353549.html

Well, actually they are NOT exponential, but exponential square or gaussian. At first glance this may seem a slight or neglectable difference but actually is just the opposite. This difference is constitutive and very critical, since it enables the existence of a transport level, and explains many features of carrier transport by hoping in disordered materials . For more information, refer to "Charge Transport in Disordered Organic Materials" by Sergei Baranovski. Cheers.

Mott characteristic temperature is in inverse relation to the wave function localization length. If the value of localization length is less, does that mean the resistivity is higher OR resistivity is less?

In disordered materials, as the localized electron wavefunction spreads or gets larger, this state is to be considered more "extended", which in turn means a higher mobility. Then, I would say that a lower localization length should mean a higher resistivity.