One needs to be very careful about trying to apply the same concepts from inorganic semiconductors to organic materials used to make devices such as photovoltaic cells.
An important example is excitons.
In inorganic semiconductors these arise from the Coulomb interaction between an electron and a hole and that have binding energies of much less than an electron Volt and they have a spatial extent of many lattice constants. They are sometimes called Wannier-Mott excitons.
Because they are so large variation of the dielectric constant of the material has a significant effect on the binding energy and spatial extent. As a first approximation one solves the hydrogen atom problem with the band effective mass and material dielectric constant.
However, the excitons (i.e., low lying singlet excited states are produced by photon absorption and can decay radiatively) in organic materials are VERY different. They are usually spatially localised on a single molecule. They are sometimes called Frenkel excitons.
The localisation can be seen by making a dilute "solution" of the molecules in a glass or matrix. They differ little from a thin film of just the molecules. The binding energy (i.e., the energy difference between the excited state and that of an electron and a hole on two neighbouring molecules) can be of the order of an electron Volt and reflects electronic correlations on the molecule. Except in very clean single crystals, there are usually no bands (and so an effective mass cannot be defined) and the dielectric constant does not determine the binding energy or the spatial extent of the exciton.
This is the question I was expecting to hear if you hadn't needed to leave the colloquium early.
ReplyDeleteWhen I first heard of this idea that the hole and the electron are Coulomb-bound, it sounded wierd to me because this is certainly not the way one talks about excitations in molecules. Where is the exchange?
This does seem important, because "charge separation" would seem to imply that the triplet must be involved somehow. Otherwise, what is "separating"?? The singlet is, as any child knows, "inseparable"... It would seem intuitively that the separated state of two electrons doesn't need to be an eigenstate of S_z or S^2.
This may be a bit out of left field, but back in the 1930's people were concerned about the conductivity of alkyl halide crystals. The idea that there is an interaction between a hole and it's particle influences conductivity etc. is discussed and calculated. Though the theories are classical, they may have bearing on this problem. Recommend reading people like Jost, Mott & Littleton and Schottky .
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