What is the relative importance of disorder and dielectric relaxation [small polarons = Marcus-Hush theory] in determining the charge mobility?

There is a nice clear and succinct review article in Chemical Reviews from 2007 by Coropceanu et al.

The view that disorder is dominant has been advocated by Bassler and collaborators, in

terms of a Gaussian density of states. This leads to a mobility with the temperature dependence

[I have not seen an analytical derivation, this seems to be based on curved fitting to the results of Monte Carlo simulations].

This is in contrast, to an activated form.

Aside: Coropceanu et al. claim "there is no full theoretical justification for such an Arrhenius like expression". I am mystified by this claim. Small polaron theory [and equivalently Marcus-Hush theory, together with the fluctuation-dissipation theorem] give such a form. Indeed, in the review article they later give such expressions.

But, that is not my main point.

It is also pointed out that

**distinguishing between these two models is difficult**

**with experimental data from a limited temperature range.**

This can be seen clearly in the Figure below taken from a 2003 paper Low-k insulators as the choice of dielectrics in Organic Field-Effect Transistors

Hence, just because one can fit the data to one of the models one should NOT conclude that model is correct. Unfortunately, this is often forgotten...

Presumably measurements down to 1 K may help distinguish the two models, although apparently these devices can malfunction at lower temperature.

I have more to say about this data, and what it may say about the charge transport mechanism, but will leave that for another day...

Hi Ross

ReplyDeleteDo you think Mott-Davis amorphous semiconductors can be well described by Marcus-Hush theory?