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

able with thermal energies at room temperature, the high temperature approximationmade in Eq. (2) is unlikely to be valid even at room temperature.In this case, it will be necessary to use more detailed theories which accountfor quantization of vibrational energy and allow nuclear tunneling betweendifferent vibrational states [17].As explained earlier, an additional reorganization energy arises whenthe nanocrystals are surrounded by a dielectric which relaxes in response tothe change in charge state of the nanocrystal. For the case considered by Brus,where silicon nanocrystals are surrounded by water, the highly polar natureof the solvent leads to a value of k o as large as 400 meV for transfer betweentouching nanocrystals of 2 nm diameter [13]. In a close-packed film of CdSenanocrystals coated with tri-n-octylphosphine oxide (TOPO), the TOPOligands (and the surrounding nanocrystals) play the role of the solvent. Forexample, we can use Eq. (5) to estimate a value of k o = 100 meV for 2-nmdiameterCdSe particles with a center-to-center separation of 3.3 nm(corresponding to the separation of close-packed TOPO-coated particles[18]). In this estimate, we have assumed that the local effective dielectricconstant is dominated by the TOPO, which has a static dielectric constante s = 2.61 [19], and we approximate the optical frequency dielectric constantwith that of TOPO, which is e opt = 2.07 [20].The |V 12 | 2 tunneling term in Eq. (1) can be treated in a simpleapproximation as tunneling through a one-dimensional potential barrier inthe presence of an applied field. This approach was used by Leatherdale et al.in the context of electron transfer from a photoexcited nanocrystal containingan electron and a hole [21]. Using the Wentzel–Kramer–Brillouin (WKB)approximation to obtain the tunneling probability through a square tunnelbarrier of height / and width d in an applied field E gives a tunneling probabilityof" rffiffiffiffiffiffiffiffiffi4 2m* 1hi#S ¼ exp3 t 2 eE /3=2 ð/ eEdÞ 3=2ð6Þwhere m* is the effective mass of the carrier within the barrier. For thin, highbarriers, the tunneling probability is found to decrease exponentially withincreasing barrier width.It is often useful to describe the charge transport properties of anextended solid in terms of the carrier mobility, l. For electron transport, forexample, the electron mobility l e is defined byJ e ¼ nel e Eð7Þwhere J e is the electron drift current density, n is the number density of electrons,and E is the applied field. In systems where hopping transportCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.