The Conduction Bands

The conduction bands are less completely and accurately described by the simplest LCAO description, as we saw in Chapter 3. Nonetheless a number of things can be learned from such a study. Wc turn to that next. 

However such carriers arc introduced, when they come to equilibrium with the lattice, they can be expected to occupy states within the thermal energy kT (25 millivolts at room temperature) of the band edges- near the bottom of the conduction band or the top of the valence band. Thus, as we discuss the conduction band, it will be desirable to focus on the states of lowest energy and it will be convenient, at the same time, to consider the states near the top of the valence band. 

The energy bands of gallium arsenide. One of the (i-ansitions that contributes to the optical absorption peak, 2, is shown. Energies are given in cV. (After Herman ct al., 1968.] 

Wc saw the general form of the valence bands in Fig. 6-1 for a number of semiconductors, and discussed the general features there. In Fig. 6-6 we show another version of the bands for GaAs, which will be useful for reference as we construct the conduction bands from LCAO theory. 

Antibonding Orbitals as a Basis for Interpreting Band Features 

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The sensitive layer of the systems under investigation eonsists of a mixture of BaFBr with Eu dotation. Other systems are available in the mean time too. X-ray- or y-quants initiate transitions of electrons in the crystal lattice. Electrons are excited from the valence band to the conduction band [2]. Electrons from the conduction band are trapped in empty Br -lattice places. They can return to the valence band via the conduction band after an excitation by... 

Electronic and optical excitations usually occur between the upper valence bands and lowest conduction band. In optical excitations, electrons are transferred from the valence band to the conduction band. This process leaves an empty state in the valence band. These empty states are called holes. Conservation of wavevectors must be obeyed in these transitions + k = k where is the wavevector of the photon, k is the... 

Semiconductors are poor conductors of electricity at low temperatures. Since the valence band is completely occupied, an applied electric field caimot change the total momentum of the valence electrons. This is a reflection of the Pauli principle. This would not be true for an electron that is excited into the conduction band. However, for a band gap of 1 eV or more, few electrons can be themially excited into the conduction band at ambient temperatures. Conversely, the electronic properties of semiconductors at ambient temperatures can be profoundly altered by the... 

The Fenni energy p which is the difference in energy between the bottom of the conduction band and... 

Figure 9.8(a) shows how the conduction band C and the empty valence band V are not separated in a conductor whereas Figure 9.8(c) shows that they are well separated in an insulator. The situation in a semiconductor, shown in Figure 9.8(b), is that the band gap, between the conduction and valence bands, is sufficiently small that promotion of electrons into the conduction band is possible by heating the material. For a semiconductor the Fermi energy E, such that at T= 0 K all levels with E < are filled, lies between the bands as shown. 

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...

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...

Fig. 2. Schematic diagram of active layer stmctures employed in LEDs under forward bias showing the conduction band (CB) and valence band (VB). The simplest devices employ (a) a homostmcture active layer wherein the bandgap is constant throughout the device. More advanced stmctures consist of (b) single and (c) double heterostmctures. Heterostmctures faciUtate the confinement and injection of carriers in the active region where the carriers may...

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. 

GaP N, is clearly evident. The addition of N shifts the peak to longer wavelengths and broadens the spectral emission. The curves for the AIGalnP LEDs represent devices of three different alloy compositions, all exhibiting recombination for the conduction band direct minimum. The emission spectmm of the blue InGaN LED exhibits uniquely broad emission, most likely as a result of recombination via deep Zn impurities levels (23). 

Fig. 1. Band-edge energy diagram where the energy of electrons is higher in the conduction band than in the valence band (a) an undoped semiconductor having a thermally excited carrier (b) n-ty e doped semiconductor having shallow donors and (c) a -type doped semiconductor having shallow acceptors.

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. 

Semiconductors can be divided into two groups direct and indirect band gap materials. In direct semiconductors the minimum energy in the conduction band and the maximum in the valence band occur for the same value of the electron momentum. This is not the case in indirect materials. The difference has profound consequences for the transitions of electrons across the band gap in which light is emitted, the radiative transitions, of interest here. 

The distributions of states in conduction and valence bands are commonly described by the effective density of states. The concentration of electrons, n, in the conduction band can be calculated as... 

Population inversion is easier to achieve when the effective density of states in the conduction band is low. 

Heterogeneous Photocatalysis. Heterogeneous photocatalysis is a technology based on the irradiation of a semiconductor (SC) photocatalyst, for example, titanium dioxide [13463-67-7] Ti02, zinc oxide [1314-13-2] ZnO, or cadmium sulfide [1306-23-6] CdS. Semiconductor materials have electrical conductivity properties between those of metals and insulators, and have narrow energy gaps (band gap) between the filled valence band and the conduction band (see Electronic materials Semiconductors). 

Fig. 1. Photoexcitation modes iu a semiconductor having band gap energy, E, and impurity states, E. The photon energy must be sufficient to release an electron (° ) iato the conduction band (CB) or a hole (o) iato the valence band (VB) (a) an intrinsic detector (b) and (c) extrinsic donor and acceptor...

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