Bulk band

At a surface, not only can the atomic structure differ from the bulk, but electronic energy levels are present that do not exist in the bulk band structure. These are referred to as surface states . If the states are occupied, they can easily be measured with photoelectron spectroscopy (described in section A 1.7.5.1 and section Bl.25.2). If the states are unoccupied, a teclmique such as inverse photoemission or x-ray absorption is required [22, 23]. Also, note that STM has been used to measure surface states by monitoring the tunnelling current as a fiinction of the bias voltage [24] (see section BT20). This is sometimes called scamiing tuimelling spectroscopy (STS). 

Resonant Excitation Excitation by a laser, which is resonant with an electronic transition of the material under investigation, can increase the Raman cross-section by approximately 10. The transitions and thus the resonance wavelengths are specific for the substances. Resonance excitation thus leads to selectivity that can be useful for suppressing bulk bands, but can also complicate the detection of mixtures of substance with different absorption spectra. 

We have reported a simple, green, bench top, economical and environmentally benign room temperature synthesis of MSe (M=Cd or Zn) nanoparticles using starch, PVA and PVP as passivating agents. The whole process is a redox reaction with selenium acting as the oxidant and MSe as the reduction product. An entire "green" chemistry was explored in this synthetic procedure and it is reproducible. The optical spectroscopy showed that all the particles are blue shifted from the bulk band gap clearly due to quantum confinement. Starch capped CdSe nanoparticles showed the presence of monodispersed spherical... 

EL spectra (peaked 820 nm) recorded from the crossed NW LEDs exhibit blueshifts relative to the bulk band gap of InP (925nm). The blueshifts are caused in part by quantum confinement of excitons, although other factors may also contribute. Furthermore, PL studies have demonstrated that the PL peak can be systematically blueshifted as the NW diameter is decreased,53 and... 

These real solutions have reduced energies (1.18) lying in the bulk band Xk < 1 (Fig. 1.3), with delocalized periodic wave functions (1.23) spread along the chain. When zs > l(zs < — 1), a real root disappears at Ok = 0(Ok = 7r), and only (N — 1) real solutions remain. To account for these lost solutions, it is necessary to take Ok complex and write... 

Returning to (1.26), with f3a 0(rj / 0), we see that it has at least (N — 1) real roots, whose corresponding wave functions are delocalized and have reduced energies in the bulk band (1.18) of width AXk = 2. The remaining two roots may both be real, so that they too lie in the band, and the system supports only delocalized states. If, however, one or both of the remaining roots have 14-values of the form (1.31), then a new situation arises, which requires further analysis. Inserting (1.31) in (1.18) gives... 

Before leaving this section, we should also mention that the location of the V- and jV-states, relative to the bulk band, depends on the sign of the bond energy / . If the AO s in the substrate are of s-(p-)symmetry, then P < 0(P > 0) and the V-(A/"-) states lie below the bulk s-(p-) band and are... 

In the ground state, the M = N/2) states in the lower-half of the bulk band are doubly occupied, so the total reduced energy for 0k — 0k — 8k) is... 

The calculated Rayleigh mode (SJ, the lowest lying phonon branch, is in good agreement with the experimental data of Harten et al. for all three metals. Due to symmetry selection rules the shear horizontal mode just below the transverse bulk band edge can not be observed by scattering methods. The mode denoted by Sg is the anomalous acoustic phonon branch discussed above. Jayanthi et al. ascribed this anomalous soft resonance to an increased Coulomb attraction at the surface, reducing the effective ion-ion repulsion of surface atoms. The Coulomb attraction term is similar for all three metals... 

Fig, 26. Experimental dispersion curve of the Kr monolayer and measured line width broadening As of the Kr creation phonon peaks. The solid line in the dispersion plot is the clean Pt(lll) Rayleigh phonon dispersion curve and the dashed line the longitudinal phonon bulk band edge of the Pt(l 11) substrate, both in the r Mn azimuth which is coincident with the r Kk, azimuth. 

Irradiation of MgO at room temperature in the presence of oxygen leads to formation of OJ and OJ (338, 355,407), which can be readily observed by EPR. This process occurs at UV energies much less than the bulk band gap, showing that surface lattice ions are involved which have a reduced band gap (1,356). On TiOz, OJ is the only stable species at room temperature, but irradiation in the presence of oxygen at 77 K (66,88,205,207,208) leads to Oj as well as O . The situation on Ti02 is very complicated (Section IV,B,1) and depends on the degree of hydroxylation of the surface (204, 205, 207, 408). 

As mentioned earlier, the existence of surface shifted core levels has been questioned.6 Calculated results for TiC(lOO) using the full potential linearized augmented plane wave method (FLAPW) predicted6 no surface core level shift in the C Is level but a surface shift of about +0.05 eV for the Tis levels. The absence of a shift in the C Is level was attributed to a similar electrostatic potential for the surface and bulk atoms in TiC. The same result was predicted for TiN because its ionicity is close to that of TiC. This cast doubts on earlier interpretations of the surface states observed on the (100) surface of TiN and ZrN which were thought to be Tamm states (see references given in Reference 4), i.e. states pulled out of the bulk band by a shift in the surface layer potential. High resolution core level studies could possibly resolve this issue, since the presence of surface shifted C Is and N Is levels could imply an overall electrostatic shift in the surface potential, as suggested for the formation of the surface states. 

In many cases there are electronic states with a strong weight in the surface layer, but which are not located in a gap of the projected bulk band structure. The electrons in these states can decay into bulk states much faster than those occupying pure surface states. These states are known as surface resonances. One of these cases occur in the Ru(0001) surface. 

The required 2D nearly free electron gas is realized in Shockley type surface states of close-packed surfaces of noble metals. These states are located in narrow band gaps in the center of the first Brillouin zone of the (lll)-projected bulk band structure. The fact that their occupied bands are entirely in bulk band gaps separates the electrons in the 2D surface state from those in the underlying bulk. Only at structural defects, such as steps or adsorbates, is there an overlap of the wave functions, opening a finite transmission between the 2D and the 3D system. The fact that the surface state band is narrow implies extremely small Fermi wave vectors and consequently the Friedel oscillations of the surface state have a significantly larger wave length than those of bulk states. 

The surface Wave function is determined from the bulk band structure of the solid. 

The CdS/ZnO interface is of particular importance in Cu(In,Ga)Se2 thin film solar cells because it is used in the standard cell configuration (Fig. 4.2). A first experimental determination of the band alignment at the ZnO/CdS interface has been performed by Ruckh et al. [102]. The authors have used ex-situ sputter-deposited ZnO films as substrates. The interface formation was investigated by stepwise evaporation of the CdS compound from an effusion cell. Photoelectron spectroscopy revealed a valence band offset of A Vb = 1.2eV. An identical value of 1.18eV has been derived using first-principles calculations [103]. With the bulk band gaps of CdS and ZnO of 2.4 and... 

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