P-Valence band

The most widely-used source is the photoemission GaAs source (Gar-win, Pierce and Siegmann, 1974 Pierce et al, 1980), the principle of which is shown in fig. 2.11. The spin—orbit interaction splits the P-valence band at the r point (fe = 0 in the plot of one-electron energy E vs momentum k) into fourfold degenerate P3/2 and twofold degenerate Pl/2 bands with a separation of 0.34 eV. 

At room temperature the pressure-induced phase transition in SmS differs from those in SmSe and SmTe in that it is discontinuous (55). It is not known whether it remains discontinuous at T=0. It was pointed out by Davis (56) that the two modes of behavior could be explained by assuming different mechanisms for the transition, i.e. an f6 - f5d delocalization in SmS and a simple Se(4p)—Sm(55) band-gap closing in the selenide and telluride. This suggestion was supported by APW calculations of the band structure of the Sm monochalcogenides. In the case of SmS the 4/states were found to lie in the band gap, but in SmSe and SmTe they were located below the p-valence bands,... 

Fig, 115. The bottom of the 5d conduction band and its exchange splitting ( red shift ) with temperature. Also shown is the top of the p valence band and the localized levels Af and 4f. (After Wachter 1986.)... 

Another question raised in ref. 85 is connected to the role of the filled d shell in the the intra- and interlayer interactions. Arguments focussing on the hybridisation of the. s and p valence bands seem to be not sufficient to describe the deviation from the ideal hep structure. 

The energy distribution curves of the photoelectron emission from cleaved single crystals at 300 K for photon energies hv = 6.5 to 9.7 eV (see Fig. 115) reveal peaks attributed to4f levels at 1.6 eV below Ep with a peak location and peak width independent of exciting photon energy, and to p states ca. 3 eV below Ep. The peak at 5.5 eV below Ep, observable only for hv>9 eV, cannot be explained it may result from scattered electrons [1,3]. Earlier studies at hv = 6.5 eV on single crystals [2] and at hv = 6.5 to 10.2 eV on (ordered) polycrystalline films [6] showed that the 4f levels lie above the p valence band but that emission from 4f is very weak. Studies with 40 eV synchrotron radiation photons reveal the intense 4f peak at 1.8 eV below Ep and a broad p band peak around 3 eV below Ep. But there also is an unidentified broad peak between 8 and 11 eV (not observable for 61 eV photons) and a weak broad peak at 13 eV below Ep (not studied for 61 eV), which was tentatively attributed to the outermost s band of selenium, Sato etal. [7]. 

The values for the paramagnetic moment of GdSe indicate that one extra electron of the Gd ion remains in the 5d state. The threefold degenerate t2g branch of the 5d band can overlap sufficiently with the 12 next-nearest Gd ions to provide a metallic bond. Thus the excess electron in (Gd3 Se3 + e") may be regarded as a conduction electron in the 5d(t2g) level [19, 20]. A model of a simple rigid conduction band is proposed in which the number of free carriers is determined by the stoichiometry [3]. Apparently, there is an energy gap between the bottom of the 5d conduction band and the top of the p valence band. Deviations from... 

Simple metals like alkalis, or ones with only s and p valence electrons, can often be described by a free electron gas model, whereas transition metals and rare earth metals which have d and f valence electrons camiot. Transition metal and rare earth metals do not have energy band structures which resemble free electron models. The fonned bonds from d and f states often have some strong covalent character. This character strongly modulates the free-electron-like bands. 

Figure 9.9 Impurity levels I in (a) an n-type and (b) a p-type semiconductor C is the conduction band and V the valence band...

Alternatively, as in Figure 9.9(b), a dopant with one valence electron fewer than the host contributes an impurity band 1 which is empty but more accessible to electrons from the valence band. An example of such a p-type semiconductor is silicon doped with aluminium KL3s 3p ) in which the band gap is about 0.08 eY... 

A semiconductor laser takes advantage of the properties of a junction between a p-type and an n-type semiconductor made from the same host material. Such an n-p combination is called a semiconductor diode. Doping concentrations are quite high and, as a result, the conduction and valence band energies of the host are shifted in the two semiconductors, as shown in Figure 9.10(a). Bands are filled up to the Fermi level with energy E. ... 

The impurity atoms used to form the p—n junction form well-defined energy levels within the band gap. These levels are shallow in the sense that the donor levels He close to the conduction band (Fig. lb) and the acceptor levels are close to the valence band (Fig. Ic). The thermal energy at room temperature is large enough for most of the dopant atoms contributing to the impurity levels to become ionized. Thus, in the -type region, some electrons in the valence band have sufficient thermal energy to be excited into the acceptor level and leave mobile holes in the valence band. Similar excitation occurs for electrons from the donor to conduction bands of the n-ty e material. The electrons in the conduction band of the n-ty e semiconductor and the holes in the valence band of the -type semiconductor are called majority carriers. Likewise, holes in the -type, and electrons in the -type semiconductor are called minority carriers. 

Fig. 2. (a) Energy, E, versus wave vector, k, for free particle-like conduction band and valence band electrons (b) the corresponding density of available electron states, DOS, where Ep is Fermi energy (c) the Fermi-Dirac distribution, ie, the probabiUty P(E) that a state is occupied, where Kis the Boltzmann constant and Tis absolute temperature ia Kelvin. The tails of this distribution are exponential. The product of P(E) and DOS yields the energy distribution... 

In an intrinsic semiconductor, charge conservation gives n = p = where is the intrinsic carrier concentration as shown in Table 1. Ai, and are the effective densities of states per unit volume for the conduction and valence bands. In terms of these densities of states, n andp are given in equations 4 and... 

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