Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

[13]. The presence of these higher-lying states allows electron transfer to occurwith a smaller activation energy than would be necessary for direct transfer tothe lowest electron state in the inverted region.Electron transfer in a nanocrystalline film is a local process sensitive tothe electronic structure of an individual nanocrystal and to its immediateenvironment. Therefore, disorder can play an important role in determiningelectron transport though the film. The first source of disorder in the electronenergy levels arises from the distribution of particle sizes, leading to adistribution of quantum confinement energies. This disorder is also responsiblefor the inhomogeneous broadening observed in absorption and emission.For typical CdSe nanocrystals, this broadening is in the range 50–100meV and is mostly due to variation in the electron confinement energy. At agiven electric field, electron transfer will occur most readily from particleswhere the neighboring particle has an electron affinity which gives the lowestactivation energy. Further disorder arises from the distribution in interparticleseparations in a solid film. Because the tunneling rate is exponentiallysensitive to the tunneling distance, a distribution of distances will lead to adistribution of tunneling rates. Also, the effective dielectric constant experiencedby a charged particle will be sensitive to the exact arrangement of otherparticles around it. Because the electron affinity depends not only on the electron-confinementenergy but also on the local dielectric environment surroundingthe nanocrystal [22] spatial disorder will give rise to additionaldisorder in the electron affinity of individual particles.The effects of disorder on the transport properties of nanocrystallinefilms have been studied for metallic particles [23], but they have not yet beenmodeled in detail for semiconducting particles. However, the results of workon charge transport in molecularly doped polymer films are particularlyrelevant because much of the physics is similar. Ba¨ssler and co-workers haveused Monte Carlo simulations to model the field and temperature dependenceof the mobility in systems with a Gaussian distribution of transport levels [24].At low fields, electrons on nanocrystals with particularly low energies withinthe broadened distribution will find it more difficult to hop to a neighboringnanocrystal, because the neighbors are likely to be higher in energy. Thepresence of these low-energy sites leads to behavior which is in some waysanalogous to the effect of traps. Ba¨ssler and co-workers assume microscopichopping rates given by the simple Miller–Abrahams model [25] (activationlesswhere the final state is lower in energy than the initial state and with anactivation energy given by DG where the hop is ‘‘up hill’’ in energy). In itssimplest form, their model predicts mobilities which follow" #A 2 h pffiffiffiil ¼ l 0 expexp cðTÞ Eð12ÞkTCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.