Materials can be classified based on the occupancy of the energy bands (Figure 13). In an insulator or a semiconductor, an energy band gap, Eg, is between the filled valence band, Ev, and the unoccupied (at 0 K) conduction band. In metals, the conduction band is partially filled (refer to Figure 13 ). Typical semicon­ductors have band gaps up to 1.5 eV; when the band gap exceeds 3.5 eV, the material is considered to be an insulator. Table 1 reports the band gaps of some important semiconductors (Ge, Si, GaAs, and SiC) and insulators (UO2, MgO, MgAl2O4, and Al2O3).

1.02.4.2 Excited States

The definition of an electronic defect is effectively ‘a deviation from the ground state electronic

3s —— —|-

configuration.’ The defects discussed in Section 1.02.4.2. were holes and electrons. Here, we consider defects in which the excited species is localized around the atom by which it was excited.

If an electron is excited into a higher lying orbital, there must be a difference between the angular momentum of the ground state and the excited state to accommodate the angular momentum of the photon that has been absorbed during the excitation process (conservation of angular momentum). For example, if the ground state is a singlet, then the excited state may be a triplet. A simple example would be 2p! 3s excitation of an oxygen ion in MgO (Figure 14).

Notice how the energy levels in Figure 14 alter their energies between the ground state and excited states. Therefore, in this case, it is not correct to estimate the energy difference between the ground state and excited states based on the knowledge of only the ground state energy configuration.

If the excitation energy is calculated based on the ground state ion positions, it is known as the Franck — Condon vertical transition. When a photon is ab­sorbed, the energy can be equal to this transition. However, the electron in the higher orbital will cause the forces between the ions to be altered. Con­sequently, the ions in the lattice will change their positions slightly, that is, relaxation will occur. Such relaxation processes are known as nonradiative, that is light is not emitted. Notice that the total energy of the system in the excited state decreases. However, if the triplet excited state now decays back to the singlet ground state (a process known as luminescence,18 see Figure 15), locally the ions are no longer in their optimum positions for the ground state. That is, the relaxed system in the ground state has become higher. The difference between the excitation energy

2p-H — +ь +ь

Ground state Excited state

Figure 14 The 2p! 3s excitation of an oxygen ion in MgO.

and the luminescence energy is known as the Stokes shift.18

Figure 16 represents an example of an excited state electron in MgO, known as a self-trapped exci — ton.19 The model uses the idea that an exciton is composed of a hole species and an excite electron. Notice that the excited electron has an orbit that is between the hole and its nearest neighboring cations. Thus, the hole is shielded from the cations. This means that the cations do not relax to the extent

they would if there was a bare hole (the small relaxa­tions are indicated by the arrows). Experimentally, the excitation energy in MgO is 7.65 eV, and the luminescence is 6.95 eV, which yields a small Stokes shift of only 0.7 eV.20

In comparison, a model for the exciton in alkali halides is shown in Figure 17. In this case, the exciton is composed of a Vk center (a hole shared between two halide ions) and an excited electron (the so-called Vk + e model). However, it is to be noted that the two halide ions that comprise the Vk center are not displaced equally from their original lattice positions. In fact, one of the halide ions is essentially still on its lattice site, while the other is almost in an interstitial site. As calculations suggest that the hole is about 80% localized on this intersti­tial halide ion, it is almost an interstitial atom known as an H-center. Also, the electron is shifted away from the hole center and is sited almost completely in the empty halide site (called an F-center). As such, the model is almost a Frenkel pair plus an electron localized at a halide vacancy (the so-called F—H pair model).

Whichever model is nearest to reality, Vk + e or F—H pair, it is clear that there is considerable lattice relaxation. This is reflected in the large Stokes shift. In LiCl, the optical excitation energy is 8.67 eV and the я-luminescence energy is only 4.18 eV, leading to a Stokes shift of 4.49 eV.21