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

dominates, the mobility is often field dependent. The mobility is related to thenet hopping rate for individual carriers, R(E), bylðEÞ ¼ RðEÞE d ð8Þwhere d is a typical hopping distance in the direction of the applied field andR(E) = R forward (E) R back (E), the difference in forward and backwardshopping rates.In some materials, a significant proportion of the carriers may occupytrap states which are much less mobile than the ‘‘free’’ carriers. It is useful todefine an effective mobility, l eff , such thatJ ¼ n total el eff Ewhere n total is the sum of both trapped and free-charge carrier densities. Wherethe trapped carriers are completely immobile and the free carriers have amobility l free , we may define the effective mobility asn freel eff ¼ l free ð10Þn totalIn nanocrystalline systems it is well known that trap states exist at thesurface of the particles and that the number and depth of traps is highlysensitive to the surface passivation. Because transport of both trappedcarriers and ‘‘free’’ carriers (those occupying core states) involves tunnelingbetween particles, carriers in shallow traps may have mobilities which are notmuch less than those of ‘‘free’’ carriers. It is therefore not possible to draw aclear distinction between mobile (free) and immobile (trapped) carriers. Inthis case, where there are populations of carrier n i with different mobilities l i ,the appropriate definition of effective mobility isXl i n iil eff ¼ Xð11Þin iIn our discussion so far we have considered only a single core electroniclevel as being involved in electron transport. We have also neglected the effectof disorder, which leads to a distribution of energy levels and interparticlespacings. In this simple model for electron transport between identicalnanocrystals, one would expect the activation barrier to decrease with appliedfield until the transfer becomes activationless at DG = k. At higher fields,the activation energy would then increase as the ‘‘inverted Marcus region’’ isentered. In practice, though, there is a series of quantum-confined electronlevels in a nanocrystal, and at high fields, electrons are likely to be injected intohigher-lying electronic states, followed by rapid relaxation to the lowest stateð9ÞCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.