Valence bands density of states

Similar equations hold for holes with n replaced by p in the subscripts, Nc by the valence-band density of states Nv, and AET = ET — Ev. The optical emission rate is related to the photoionization cross section ([Pg.9]

To solve for the Fermi energy we must return to Eq. (B7). First consider the case NIk — 0, i.e., no states in the band gap. Then the total number of electrons in the system is NWi (the total valence-band density of states) and thus n + (ATv, — p) = Nyt, orp = nsn , the intrinsic concentration. Thus,... 

Fig. 3.3 shows one calculation of the valence band density of states of a-Si H compared with the equivalent results for crystalline Si (Biswas et al. 1990). This is a tight binding calculation using the 216 atom cluster model created by Wooten, Winer and Weaire (1985). The... 

The probability of electron emission into the vacuum jumps abruptly at the work function energy, vao J l d is approximately constant above this energy, so that the valence band density of states is given by dT(A[Pg.71]

Fig. 3.9. Photoemission yield measurements of the valence band density of states. Note the exponential band tail and linear valence band edge (Winer and Ley 1989).

Optical transitions between the valence and conduction bands are responsible for the main absorption band and are the primary measure of the band gap energy. The optical data are also used to extract information about the band tail density of states. However, the absorption coefficient depends on both conduction and valence band densities of states and the transition matrix elements and these cannot be separated by optical absorption measurements alone. The independent measurements of the conduction and valence state distributions described in Section 3.1.1 make it possible to extract the matrix elements and to explore the relation between N E) and the optical spectrum. 

Fig. 4.23. There has not been a similar deconvolution of the defect absorption in p-type material using the measured valence band density of states, but E fC) is estimated to be about 0.9 eV. The mobility gap is about 1.85 eV (see Fig. 3.16), so that (/—21F 0.1eV with an uncertainty of about 0.2 eV. This result is consistent with a correlation energy of 0.2 eV and a small relaxation energy. However, other investigators, with essentially the same data but different procedures for extracting the energies, have obtained negative values of the...

Fig. 6.12. The distribution of formation energies according to the weak bond model. The shape is proportional to the valence band density of states.

We wish to compare the valence band density of states (DOS) of f.c.c. and h.c.p. metals with and without stacking faults. We therefore adopt a mixture of the f.c.c. and h.c.p. structures as a representative of the stacking fault structure of either of these structures. To calculate the DOS we summed up the squares of the coefficients of molecular orbital wave functions and convoluted the summed squares with the Gaussian of full width 0.5 eV at half maximum. For these DOS calculations we chose the metals Mg, Ti, Co, Cu and Zn. The model clusters employed here for both the f.c.c. and the h.c.p. structures were made of 13 atoms i.e., a central atom and 12 equidistant neighbor atoms. These structures are shown in Fig. 1. We reproduced the typical electronic structures in bulk materials by extracting the molecular orbitals localized only on the central atom from all the molecular orbitals which contributed - those localized on ligand atoms as well as on the central atom. To perform calculations we take the symmetry of the cluster as C3, and the number... 

When, in an Auger transition, one or both of the final state holes lie in the valence band of a solid, the spectrum observed is simply the selfconvolution of the valence band density of states (DOS) so the shape of a core-valence (core W) AES profile should contain information about the valence band. Chemisorption induces modifications of the local DOS at the surface that lead to changes in the line shapes of the ejected electrons ( fine structure )) for example, sulfur as a monolayer on a Ni(lOO) surface in the structure c(2 x 2) S is characterized as having a residual d-band... 

Another interesting comparison is with the optical absorption tail. In principle, the optical absorption coefiicient is a convolution of the valence-band density of states with the conduction-band density of states multiplied by a matrix element. However, if the band tails are exponential and one band tail is broader than the other, an elementary mathematical analysis shows that the optical absorption tail has the same energy dependence as the broader band tail, with the energy dependence of the matrix element neglected. In our picture of the electronic structure of a-Si H, the valence-band tail is broader, and hence the characteristic width of the absorption tail should be compared with the width of the valence-band tail ( 42 meV). The optical absorption tail for material prepared under conditions similar to the... 

UPS (Ultraviolet photoelectron spectroscopy), is similar to ARUPS but spectra are collected at a fixed angle to determine the sample s overall valence band density of states (DOS). UPS is not restricted to single crystal samples. SPUPS (Spin polarised UPS) allows the density of states to be determined independently for the spin-up and spin-down electrons of a magnetic material by using a polarisation sensitive detector. 

By combining the electron energy analyser with a polarization sensitive Mott Detector separate spin-up and spin-down valence band density of states spectra can be produced for magnetic samples. This technique is known as spin polarised ultraviolet photoelectron spectroscopy (SPUPS). 

Using this technique Lang et al. (1981) have mapped the valence band density of states in rare earth metals. Due to long counting times necessary to acquire a BIS spectrum extensive beam damage effects are expected to occur. This confines the application of BIS at present to clean metal surfaces. Nevertheless, the exact determination of the density of unoccupied states yields very valuable information for reaction studies as pointed out, for instance, in section 3.1.3. 

The 4f levels of rare earth metals remain in general unaffected by oxidation due to their largely atomic-like nature. The map of the 4f and valence band density of states, however, presented by Lang et al. (1981), shows 4f levels in critical proximity to the Fermi level for Ce (1.9 eV below Ep), Eu (1.5 eV below Ef), Yb (1.3 eV below Ep), Sm (0.5 eV above Ep) and Tm (1.1 eV above Ep). Thus, due to changes in the chemical environment, the external pressure or by... 

The conduction and valence band density of states coefficients in Si are given by [4.68]... 

Fig. 27. Experimental and calculated valence band density of states for CePdj (Aekermann 1984).

Fig. 32. XPS/BIS valence band density of states for insulating Ce02, mixed valent CeN, and heavy fermion CeSi2 (Wuilloud et al. 1984a, 1985).

Figure 1.6 Valence band density of states of sublimed films of Cgo and C70 on a gold substrate from UV photoemission studies. (From Santra, A. K. etal., Solid State Commun., 85, 77, 1993. With permission.)...

We can circumvent the issue of the Fermi energy by noting that a similar definition can be made based ni=p, and with a similar definition for the effective valence-band density of states, Ny ... 

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