Valence band maximum

Eig. 1. Representation of the band stmcture of GaAs, a prototypical direct band gap semiconductor. Electron energy, E, is usually measured in electron volts relative to the valence, band maximum which is used as the 2ero reference. Crystal momentum, is in the first BriUouin 2one in units of 27r/a... 

The relevance of the indirect minima E- and E are in determining the transport properties of the material. For all of the A1 compounds and GaP, the lowest conduction band is at X and the valence band maximum is at F. The other bands foUow in the order E- >. This is the same relative... 

Flat-Band Potentials and Positions of the Valence Band Maximum Evs and Conduction Band Minimum Ecs of Oxide Semiconductors, Group IV and III/V Semiconductors, and Mixed Oxide Semiconductors with Respect to the H+/H2 Scale, Where Minus Represents above Zero and Plus Represents below Zero... 

Direct splitting of water can be accomplished by illuminating two interconnected photoelectrodes, a photoanode, and a photocathode as shown in Figure 7.6. Here, Eg(n) and Eg(p) are, respectively, the bandgaps of the n- and p-type semiconductors and AEp(n) and AEF(p) are, respectively, the differences between the Fermi energies and the conduction band-minimum of the n-type semiconductor bulk and valence band-maximum of the p-type semiconductor bulk. lifb(p) and Utb(n) are, respectively, the flat-band potentials of the p- and n-type semiconductors with the electrolyte. In this case, the sum of the potentials of the electron-hole pairs generated in the two photoelectrodes can be approximated by the following expression ... 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

For H at T in Ge, Pickett et al. (1979) carried out empirical-pseudopotential supercell calculations. Their band structures showed a H-induced deep donor state more than 6 eV below the valence-band maximum in a non-self-consistent calculation. This binding energy was substantially reduced in a self-consistent calculation. However, lack of convergence and the use of empirical pseudopotentials cast doubt on the quantitative accuracy. More recent calculations (Denteneer et al., 1989b) using ab initio norm-conserving pseudopotentials have shown that H at T in Ge induces a level just below the valence-band maximum, very similar to the situation in Si. The arguments by Pickett et al. that a spin-polarized treatment would be essential (which would introduce a shift in the defect level of up to 0.5 Ry), have already been refuted in Section II.2.d. 

Referring to Figure 3, evidence exists for placement of the Fermi levels (chemical potentials) of the redox reactions involving Hzr H2O and O2 roughly at the positions shown relative to the energies of the conduction band minimum and valence band maximum of the semiconductor, E and E, respectively. This picture takes the electron in a vacuum at infinity as the zero of energy. On this basis, the Fermi level for the reaction... 

While silicon is not the ideal solar cell material, it currently dominates the solar PV market due to its prevalence in the microelectronics industry. Crystalline silicon (c-Si) is an inorganic semiconductor, in which the valence-band maximum and conduction-band minimum are not directly aligned in Uspace, making c-Si an indirect bandgap material. The indirect nature of the bandgap in c-Si means that a considerable change in momentum is required for the promotion of an electron from... 

In equation 3, ran is the effective mass of the electron, h is the Planck constant divided by 2/rr, and Eg is the band gap. Unlike the free electron mass, the effective mass takes into account the interaction of electrons with the periodic potential of the crystal lattice thus, the effective mass reflects the curvature of the conduction band (5). This curvature of the conduction band with momentum is apparent in Figure 7. Values of effective masses for selected semiconductors are listed in Table I. The different values for the longitudinal and transverse effective masses for the electrons reflect the variation in the curvature of the conduction band minimum with crystal direction. Similarly, the light- and heavy-hole mobilities are due to the different curvatures of the valence band maximum (5, 7). 

Figure 39 Band structure of the (a) fully saturated and (b) partially saturated Si[i]-SiC>2(0 01) SL projected along the two symmetry directions of the 2D Brillouin zone of the (0 01) surface. K and M represent, respectively, the k-points in the corner and in the middle of the side of the 2D Brillouin zone. A self-energy correction of 0.8 eV has been added to the conduction states. Energies (in eV) are referred to the valence band maximum.

In LCAO1 theory the valence band maximum of a tetrahedrally bonded semiconductor is derived from the anion p-levels and its energy given by [89] ... 

Fig. 1.10. Band alignment between II-VI compounds according to density functional theory calculations by Wei and Zunger [95]. The energy of the valence band maximum of ZnS is arbitrarily set to 0 eV. A comparison to experimental results is presented in Fig. 4.18 in Sect. 4.3.1 (page 150)...

Fig. 4.1. Example energy band diagrams for a semiconductor/metal contact and and a semiconductor p/n-heterocontact. The Schottky barrier height for electrons B,n is given by the energy difference of the conduction band minimum Ecb and the Fermi energy Ey. The valence and conduction band offsets A/ An and AEcb are given by the discontinuities in the valence band maximum Eyb and the conduction band minimum, respectively...

The core and valence levels in Fig. 4.6 show comparable binding energy shifts in dependence on deposition conditions. The shifts are mainly due to shifts of the Fermi level position at the surface. The Fermi level position with respect to the valence band maximum is directly measured as the binding energy of the valence band maximum. Values for magnetron-sputtered ZnO and ZnO Al thin films are shown in Fig. 4.12 in dependence on oxygen content in the sputter gas and substrate temperature. 

Fig. 4.12. Valence band maximum binding energies of magnetron sputtered ZnO and ZnO Al films in dependence on the oxygen content in the sputter gas at room temperature (left) and in dependence on substrate temperature for deposition in pure Ar (right). The binding energies are derived from X-ray excited valence band spectra. All films were deposited using a total pressure of 0.5 Pa, a sputter power density of 0.74 Wcm 2 and a substrate to target distance of 10 cm. The horizontal line indicates the position of the conduction band minimum...

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