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

and ionization potential through two main pathways [22]. Both processestend to destabilize excess charge on a quantum dot with respect to a bulksemiconductor (the absolute value of the electron affinity is decreased,whereas that of the ionization potential is increased). The first effect is thatof quantum confinement, which requires an increase in the kinetic energy ofthe carriers as the particle diameter is decreased. The second contribution is aclassical polarization effect. Because the organic surface ligands and matrixsurrounding a chemically prepared nanocrystal have a dielectric constant thatis usually considerably smaller than that of the inorganic semiconductor(e rf2 versus e rf10), the dielectric stabilization provided by the semiconductordecreases and hence the energy required to charge the nanocrystalincreases for smaller particles. Detailed calculations of the effects of bothquantum confinement and dielectric confinement on the excitonic and singleparticleenergy levels can be found in the literature [42–46]. For the experimentalistinterested in a quick ‘‘back-of-the-envelope’’ calculation of a particle’sredox potentials based on optical data, an estimate for the shifts of thelowest single-particle electron and hole levels can be obtained from a knowledgeof the bulk semiconductor EA and IP by partitioning the experimentallyobserved bandgap change between the conduction and valence band statesusing the ratio of the carriers’ effective masses:m hEA QD ¼ EA BulkDEð15Þm e þ m hIP QD ¼ IP Bulk þm eDEð16Þm e þ m hwhere EA QD and EA Bulk , and IP QD and IP Bulk are electron affinities andionization potentials of the quantum dot and bulk material, respectively, andDE is the experimentally determined increase in the optical gap with respect tothe bulk. Equations (15) and (16) will likely provide a lower limit for thechange in the EA and IP of the quantum dot material compared to the bulksemiconductor. This is because we have ignored the polarization effectsdiscussed earlier, as well as the electron–hole Coulomb contribution to theshift of the optical gap (which will tend to reduce the optical gap with respectto the single-particle gap). Because a straightforward infinite-barrier effectivemassapproximation will invariably overestimate the kinetic energy ofconfinement, combining polarization and particle-in-a-sphere terms [22]provides a rough upper limit for the difference between the quantum-dotEA or IP and the corresponding bulk conduction or valence band edge of theformt 2 p 22m*r 2 þ 1 e 2 1 1ð17Þ2r 4pe 0 e matrix e scCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.