Thursday, May 28, 2009

A simple transport criterion for the absence of energy bands

A lot of papers on materials for organic electronics and photonics will discuss transport and optical properties in terms of conduction and valence bands, concepts that are valid and useful for inorganic crystalline semiconductors.

But, I do not think such bands exist for most of these materials. This can be seen from the magnitude of the transport mobility. These notes show a simple self-consistency argument which shows that if band transport is meaningful (i.e., one can talk about electrons with a definite wavevector and which are occasionally scattered) then the mobility must be much larger than about
e a^2/hbar ~1 cm^2/Vsec.

I derived this result over a year ago but then discovered this appears to have been well known back in the 70's, and seems to have been forgotten.

For example, the result is clearly stated:

in equation (24) of a 1963 paper by Glarum.

in equation (224) on page 24, of a classic 1971 review of Metallic Oxides by John Goodenough

page 346, of the second edition of Pope and Svenberg's Electronic processes in organic crystals and polymers.


  1. Hey Ross

    Is this also true for amorphous semiconductors? Or does a different criteria apply?

  2. If there is band transport then the mobility must be much larger than 1 cm^2/Vsec.
    Hence, whenever the mobility is less than this there can be no bands. Thus this criteria can be used to show the absence of band transport in any material.

    But, in amorphous inorganic semiconductors there may be energy bands, i.e., a broad range of energy eigenstates, which are filled and unfilled. However, these states will NOT be associated with Bloch wave vectors and charge transport will occur via incoherent hopping between these states, most of which will be localised rather than delocalised.

  3. Also see

    Mobility Gaps: A Mechanism for Band Gaps in Melanins, John E. McGinness
    Science, New Series, Vol. 177, No. 4052 (Sep. 8, 1972), pp. 896-897


    Historically, polyacetylene and its derivatives were called "melanins"

  4. I believe this notion goes back to Mott. At least, he mentioned it in his Nobel speech (as well as the fact that not everybody believed him).