Screening band estimate

Correlation energy differences (ion), 4f excitation energies A (4f ion) calculated for ionized (unscreened) final states, and screening energy estimates d,(band) and d,(atom). The initial states are the ground metallic configurations. All energies in eV. 

The sharp drop in the core-hole electron attraction U compared to the bulk value (AU, Figure 3) around N = 4.5 and 6.5 for the basic and acidic supports respectively is obviously due to the onset of the insulator to metal transition. The size of AU (= 3.5 eV) for the very small clusters is consistent with previous estimates of U(5d5d) = 3-6 eV for the nearly filled 5d band transition metals when efficient metallic screening is shut off. Most interesting is the large difference in the behavior of the core-hole electron attraction for the basic vs. acidic supports. This difference dramatically reveals the importance of the support in determining the nature and onset of the metal-insulator transition. It provides direct experimental evidence for a metal-support interaction. 

The amplitude and spatial dimensions of the potential fluctuations are different in undoped, doped, and compensated a-Si H. The band tail electrons and holes provide the mobile screening charge in doped a-Si H and the doping dependence of the potential fluctuations can be estimated from the experimental data. The magnitude of n. depends on the thermal equilibrium state, but is usually about 10 % of the donor and defect density. According to the square root law for doping,... 

For the case where the bandwidth or the warping, i. e., the transfer integral tb, respectively fi in (2.2)), is small the Coulomb repulsion between the electrons becomes important. A limited screening of the electron charge in a narrow band due to restricted electron movement can lead to a localized electron lattice, a so-called Wigner crystal. This, in fact, has been observed in the strongly ID material TTF-TCNQ where in addition to the 2A p Peierls lattice distortion a 4fcp modulation was found [48, 49, 50]. The estimated value for the on-site Coulomb repulsion U in TTF-TCNQ is U/Atb — 0.9 extracted from the frequency dependence of the NMR relaxation time [51] and the susceptibility above the Peierls transition [52]. 

An important extrinsic effect is screening by the environment, and again, this significantly alters the energy of excited states. States with larger binding energy are less screened than those that are weakly bound. Current estimates are that the n = 1 exciton solvates by ca. 0.3 eV, the n = 2 exciton solvates by ca. 0.6 eV, and the band gap solvates by ca. 1.5 - 2.0 eV (Moore and Yaron 1998). This effect will be discussed in Chapter 9. 

The composition of the arrays is often given in terms of the relative amounts of the species dispensed, for example, the number of drops of each solution. The actual compositions of the drops can be determined, for example, by x-ray photoelectron spectroscopy (XPS). The transparent FTO substrate, while not important in the screening, as discussed later, does make it possible to characterize spots spectroscopically, as shown in Figure 16.16, where the absorbance spectra can be used to estimate the band gaps of the spot materials. ... 

---