Conduction band minimum

Fig. 1. Schematic diagram of semiconductor materials showing band gaps where CB and VB represent the conduction band and valence band, respectively and 0 and 0, mobile charge. The height of the curve represents the probabiUty of finding an electron with a given momentum bound to an N-isoelectronic impurity, (a) Direct band gap the conduction band minimum, F, is located where the electrons have 2ero momentum, ie, k = 0. The couples B—B, D—A, B—D, and B—A represent the various routes for radiative recombination. See text, (b) Indirect band gap the conduction band minimum, X, is located...

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

Near a conduction band minimum the energy of electrons depends on the momentum ia the crystal. Thus, carriers behave like free electrons whose effective mass differs from the free electron mass. Their energy is given by equation 1, where E is the energy of the conduction band minimum, is the... 

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. 

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... 

The abbreviations mn and m L denote the longitudinal and transverse effective electron masses, respectively. m is the effective mass for isotropic conduction band minimum. 

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 8. Schematic representations of p-n junctions and corresponding energy band diagrams under various conditions (a) uniformly doped p-type and n-type semiconductors before junction is formed, (b) thermal equilibrium, (c) forward bias, and (d) reverse bias. Abbreviations are defined as follows Ec, electron energy at conduction band minimum E, , electron energy at valence band minimum IF, forward current Vf, forward voltage Vr, reverse voltage ...

D hexagonal BZ corresponds to the T-X direction of the three-dimensional face-centered cubic BZ where the bulk Si conduction band minimum occurs. For Ge films, instead, there is a well resolved conduction band minimum at the T point, thus indicating direct band gap character. 

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...

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...

The electron affinity of a semiconductor relates the vacuum level to the conduction band minimum at the surface. An informative way to view the electron affinity is as the conduction band offset between the semiconductor and vacuum. The band structure of the vacuum is simply the parabolic free electron bands, and the minimum energy (or vacuum level) refers to an electron at rest. For most materials, an electron at the bottom of the conduction band is bound to the material by a potential barrier of several volts. This barrier is the electron affinity and is defined as a positive electron affinity. In some instances, the vacuum level can actually align below the conduction band minimum. This means that an electron at the minimum of the conduction band would not see a surface barrier and could be freely emitted into vacuum. This situation is termed a negative electron affinity. 

The photothreshold measurements were also employed to explore the effects of surface adsorbates [7]. It was found that exposure of the GaN surface to caesium and oxygen resulted in significant lowering of the electron affinity. In feet the results suggest that the vacuum level aligns from near the conduction band minimum to 1.5 eV below the conduction band minimum. The results thus suggested an electron affinity for the caesiated surfaces that ranged from 0 to -1.5 eV. 

While EQN (1) can be used to verify an NEA for wide bandgap semiconductors, another aspect that signals the presence of an NEA is the appearance of a sharp peak at the low kinetic energy end of the spectrum. This feature is attributed to electrons thermalised to the conduction band minimum. For a positive electron affinity, these electrons would be bound in the sample and not observed in the spectrum. 

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